1. CHAPTER 2:
NUMBER
PATTERNS
AND
SEQUENCES
By: NURSYAFIKA BINTI MOHD SHAHADAN

5.  Number Patterns and Sequences
(Corak/Pola Nombor dan
Urutannya)
 Odd and Even Numbers (Nombor
Ganjil dan Genap)
 Prime Number (Nombor Perdana)
 Factors (Faktor)
 Prime Factors (Faktor Perdana)
 Multiples (Gandaan)
 Multiples and Lowest Common
Multiple, LCM (Gandaan Sepunya
dan Gandaan Sepunya Terkecil,
GSTK)

6. Number Patterns and
Sequences
(Corak/Pola Nombor
dan Urutannya)

7. sequence
The numbers are arranged in a specific
pattern known as the order.
Pattern number
Pattern sequence number can be
determined by add, subtract, multiply
or divide 'previous numbers in the
sequence', with the number / certain
numbers.

8. Fibonacci Sequence
Mathematicians have studied the pattern for
centuries. Patterns of numbers 1, 1, 2, 3, 5, 8, ...
are called the Fibonacci sequence.
This sequence begins with 1, 1 and each after the
term of the latter, obtained by adding the two
terms before appearing in the thread.

9. Describe patterns / pattern sequence of numbers
Illustrate the trend of each following sequence of numbers:

10. Odd and Even
Numbers
(Nombor Ganjil
dan Genap)

11. Odd number
Numbers 1, 3, 5, 7, ... known as an odd
number.
even number
Number 2, 4, 6, 8, ... known as an even
number.

12. Identify and explain the odd and even numbers.
Example 1: Example 2:
Identify and specify all odd and even
numbers appearing in the sequence of 3+5=8
numbers 16, 21, 26, 31, ..., 71. 7 + 13 = 20
19 + 25 = 24
Answer:
Odd numbers are 21, 31, 41, 51, ​61 General statement about
and 71. These numbers form a the amount / sum of two
sequence of numbers obtained by odd numbers:
adding 10 to the previous number.
Odd number + Odd
Even numbers 16, 26, 36, 46, 56 and Number = Even Number
66. These numbers form a sequence * The sum of two odd
of numbers obtained by adding 10 to numbers is an even
the previous number. number.

13. Prime Number
(Nombor
Perdana)

14. Prime number
whole number that can only be divided by itself and
the number 1 (the number itself and number 1). Thus,
a prime number has only two divisor (the number
itself and the number 1).
The smallest prime number is a number 2, the only
even number that is prime.
Primes less than 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43 and 47.
Number 1 is NOT a prime number (NOT a prime
number).

15. Determine whether a given number is a prime number
example:
Determine whether the following numbers are prime numbers.
13 51
Answer: Answer:
13 ÷ 1 = 13 51 ÷ 1 = 51
13 ÷ 13 = 1 51 ÷ 3 = 17
13 can only be divided 51 ÷ 17 = 3
by 1 and 13 → (2 51 ÷ 51 = 51
dividers / divisors) 51 is divisible by 1, 3, 17
Thus, 13 is a prime and 51 → (4 divider /
number. divisors)
Therefore, 51 is not a prime
number.

16. Factors (Faktor)

17. Factor
a whole number that is given is that
the number is a multiple of the
number accurately.
1 and itself is a factor of any given
number.

18. Find all the factors of:
18 50
Answer: Answer:
18 ÷ 1 = 18 50 ÷ 1 = 50
18 ÷ 2 = 9 50 ÷ 2 = 25
18 ÷ 3 = 6 50 ÷ 5 = 10
18 ÷ 6 = 3 50 ÷ 10 = 5
18 ÷ 9 = 2 50 ÷ 25 = 2
18 ÷ 18 = 1 50 ÷ 50 = 1
18 can be divided by 1, 2, 3, 50 can be divided by 1, 2, 5,
6, 9 and 18. Therefore, the 10, 25 and 50. Therefore,
factors of 18 are 1, 2, 3, 6, 9 the factors of 50 are 1, 2, 5,
and 18. 10, 25 and 50.

19. To determine whether a number is a whole number of factors
to another.
example:
Determine whether;
7 is a factor of 119.
Answer:
119 ÷ 7 = 17
119 can be divided exactly by 7. Thus, 7 is a factor of 119.
4 is a factor of 599.
Answer:
599 can not be divided exactly by 4. Therefore, 4 is not a factor
to 599.

20. Prime Factors
(Faktor
Perdana)

21. Prime factor
prime factors for a whole number is, the prime
factors of the number.
Identify the prime factors of a list of factors.
example:
Given 1, 2, 4, 7, 8, 14 and 56 are the factors of 56.
Identify all the prime factors of 56.
Answer:
Among the factors of 56, 2 and 7 is a prime
number. Therefore, the prime factors of 56 are 2
and 7.

22. Finding the prime factors of whole numbers.
example:
Get a prime factor numbers: 100
Method 1 Method 2 Method 3
List all the factors of Using the algorithm Using a diagram
100. (repeated division by trees (factor tree
Factor of 100 are 1, 2, prime factors). diagram).
4, 5, 10, 20, 25, 50
and 100. Among all
these factors, 2 and 5
are prime numbers.
Therefore, the prime Therefore, the prime
factors of 100 are 2 factors of 100 are 2 From the diagram,
and 5. and 5. the prime factors of
100 are 2 and 5.

23. Multiples (Gandaan)

24. Multiples
Multiples of a whole number is the product of the
number of any other whole number, except zero
(zero).
Multiple of the number n is in the form nk, where k
= 1, 2, 3, 4, ...
For example, multiple 3 = 3 x 1, 3 x 2, 3 x 3, 3 x 4, ..
Whole number is
divisible by another
number if the balance
is zero.

25. Divisibility Test
DIVIDER METHOD EXAMPLE
2 The last digit (unit value of) a number is 0, 2, 4, 6 90, 152, 3 866, 5 478
or 8.
3 The sum of all the digits is divisible by 3. 249
(2 + 4 + 9) ÷ 3
= 15 ÷ 3 = 5
4 Number formed by the last two digits of the 7 216
number is divisible by 4 or is zero. 16 ÷ 4 = 4
5 The last digit (unit value of the) number is 0 or 5. 480, 3 625
6 The number is divisible by 2 and 3. 738
(7 + 3 + 8) ÷ 3
= 18 ÷ 3 = 6
8 Number formed by the last three digits of the 53 288
number is divisible by 8.
9 The sum of all the digits is divisible by 9. 4 302
(4 + 3 + 0 + 2) ÷ 9
=9÷9=1
10 The last digit (unit value of the) number is 0. 560, 29 710

26. Lists multiples of whole numbers
Example 1:
List the first five multiples;
2 15
Answer: Answer:
= 2 x 1, 2 x 2, 2 x 3, 2 x 4, 2 x 5 = 15 x 1, 15 x 2, 15 x 3, 15 x 4,
= 2, 4, 6, 8, 10 15 x 5
= 15, 30, 45, 60, 75
5
Answer: * The gain of the given numbers
= 5 x 1, 5 x 2, 5 x 3, 5 x 4, 5 x 5 also form a sequence of
= 5, 10, 15, 20, 25 numbers.
9
Answer:
= 9 x 1, 9 x 2, 9 x 3, 9 x 4, 9 x 5
= 9, 18, 27, 36, 45

27. To determine whether a number is divisible by another number.
Example 2:
Determine whether 63 is divisible by;
7
Answer:
63 ÷ 7 = 9 ← 63 = 7 x 9
Thus, 63 is a multiple of 7.
8
Answer:
63 ÷ 8 = 7, the remaining 7
Therefore, 63 is not a multiple of 8.
** If the number is divisible by the number m, then n is a
multiple of m.

28. Example 3:
Use divisibility test to determine whether it is a gain of 639
234;
4
Answer:
Last two digits of 639 234, which is 34, can not be divided by
4.
Thus, 639 234 not a multiple of 4.
9
Answer:
6 + 3 + 9 + 2 + 3 + 4 = 27
The sum of all digits of 639234 is divisible by 9.
Thus, 639 234 is a multiple of 9.

29. Multiples and
Lowest Common
Multiple, LCM
(Gandaan Sepunya
dan Gandaan
Sepunya Terkecil,

30. Common multiples
Common Multiples given set of whole numbers is a
multiple of each number in the set.
Lowest common multiples (LCM)
Lowest Common Multiple (LCM) of some given number
is the smallest common multiple of the numbers.
* The concept of 'multiple' and 'factor' is a contradiction.
for example;
30 is a multiple of 1, 2, 3, 5, 6, 10, 15 and 30.
Meanwhile, 1, 2, 3, 5, 6, 10, 15 and are factors of 30.

31. Finding common multiples of two or three whole numbers.
Example 1:
Get common multiple of;
3 and 4.
Answer:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
Common multiples of 3 and 4 are 12, 24, 36, ...
2, 3 and 6.
Answer:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
Multiples of 6: 6, 12, 18, ​24, 36, ...
Common multiples of 2, 3 and 6 are 6, 12, 18, ...
** List some common multiples of whole numbers is also a sequence
of numbers.

32. To determine whether a number is a common multiple of two or three
whole numbers that are given.
Example 2:
Determine whether;
84 is a common multiple of 5 and 7.
Answer:
84 ÷ 5 = 16 remainder 4
84 ÷ 7 = 12
84 can not be divisible by 5.
Therefore, 84 is not a Common Multiples of 5 and 7.
432 is a common multiple of 6, 8 and 9.
Answer:
432 ÷ 6 = 72
432 ÷ 8 = 54
432 ÷ 9 = 48
432 is divisible by 6, 8 and 9.
Therefore, 432 is Common Multiples of 6, 8 and 9.

33. Determine LCM of two whole numbers.
Example 3:
Find the Least Common Multiples for;
9 and 12
Answer:
Method 1: Method 2:
Factoring Prime (Prime Factorisation) Use the algorithm (repeated division by prime
factors)
LCM for 9 and 12 = 3 x 3 x 2 x 2 = 36 LCM for 9 and 12 = 3 x 3 x 2 x 2 = 36

34. Example 4:
Determine LCM for;
6, 15 and 18. 14, 28 and 49.
Answer: Answer:
LCM 6, 15 and 18 = 2 x 3 x 3 x 5 LCM for 14, 28, 49 = 7 x 2 x 2 x 7
= 90 = 196

35. Common Factors and
Highest Common
Factor, HCF (Faktor
Sepunya dan Faktor
Sepunya Terbesar,
FSTB)

36. Common factors
Common Factors some whole number is a number
that is a factor of each of those numbers.
Highest common factor (hcf)
Highest Common Factor (HCF) number assigned
number is the largest number that is a factor of each
of those numbers.

37. Finding a common factor of two or three whole numbers.
Example 1:
Find the common factors;
18 and 54.
Answer:
Factors of 18: 1, 2, 3, 6, 9, 18
Factor of 54: 1, 2, 3, 6, 9, 18, 27, 54
Common factors of 18 and 54 are 1, 2, 3, 6, 9 and 18.
9, 15 and 21.
Answer:
Factor of 9: 1, 3, 9
Factor of 15: 1, 3, 5, 15
Factor of 21: 1, 3, 7, 21
Common factor of 9, 15 and 21 are 1 and 3.

38. To determine whether a number is a factor common to two or
three given numbers.
Example 2:
Determine whether;
12 is a common factor of 84 and 156.
Answer:
84 ÷ 12 = 7
156 ÷ 12 = 13
Thus, 12 is a common factor of 84 and 156.
4 is a common factor for 32, 70 and 112.
Answer:
32 ÷ 4 = 8
70 ÷ 4 = 17 remainder 2
112 ÷ 4 = 28
Therefore, 4 is not a common factor of 32, 70 and 112.

39. Determine the Greatest Common Factor of two whole numbers.
Example 3:
Get the highest common factor of;
28 and 32.
Answer:
Method 1: Method 2:
List all the factors for each Use the algorithm (repeated
number. division by a common factor).
Factors of 28: 1, 2, 4, 7, 14, 28
Factor of 32: 1, 2, 4, 8, 16, 32
Therefore, the HCF of 28 and
32 is 4.
Greatest common factor of
28 and 32 is = 2 x 2 = 4.

40. Example 4:
Get the highest common factor (HCF) for;
40, 48 and 56. 70, 84 and 126.
Answer: Answer:
* Distribution discontinued as * Distribution discontinued as
5, 6 and 7 have no common 5, 6 and 9 have no common
factors other than 1. factors other than 1.
Thus, the HCF for 40, 48 and Thus, the HCF for 70, 84 and
56 126
=2x2x2 =2x7
=8 = 14

43. Number Patterns and
Sequences (Corak/Pola
Nombor p, q, Urutannya)
19, 38, dan 304, ….. is a
number sequence.
Evaluate p + q.
a. 76
b. 152
c. 228
d. 310

44. Odd and Even Numbers (Nombor
State whether each of the following
numbers is an even number.
(a) 17 (c) 44
(b) 60 (d) 95

45. Prime Number (Nombor Perdana
Find the sum of all the prime
numbers which are less than
10.

46. Factors (Faktor)
Determine whether 9 is a factor
of the following numbers.
(a) 144 (b) 322

47. Prime Factors (Faktor Perdana)
Determine which of the
following are prime factors of
84.
(a) 3 (b) 21

48. Multiples (Gandaan)
Determine whether 592 is a
multiple of
(a) 2, (b) 3, (c) 4.

49. Multiples and Lowest
Common Multiple, LCM
(Gandaan Sepunya dan
Gandaan Sepunya Terkecil,
Which of the following numbers is
GSTK) common multiple (LCM)
the lowest
of 12, 32 and 48?
a. 96
b. 192
c. 284
d. 384

50. Common Factors and Highest
Common Factor, HCF (Faktor
Sepunya dan Faktor Sepunya
Terbesar, FSTB)
Find the highest common factor
(HCF) of 16, 24 and 32.
a. 2
b. 4
c. 8
d. 16