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Mathematics

Find the prime factorisation of the following numbers:
(i) 72
(ii) 172
(iii) 450
(iv) 980
(v) 8712
(vi) 13500

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Answer

(i) 72

2	72
2	36
2	18
3	9
3	3
	1

Hence, 72 = 2 × 2 × 2 × 3 × 3.

(ii) 172

2	172
2	86
43	43
	1

Hence, 172 = 2 × 2 × 43.

(iii) 450

2	450
3	225
3	75
5	25
5	5
	1

Hence, 450 = 2 × 3 × 3 × 5 × 5.

(iv) 980

2	980
2	490
5	245
7	49
7	7
	1

Hence, 980 = 2 × 2 × 5 × 7 × 7.

(v) 8712

2	8712
2	4356
2	2178
3	1089
3	363
11	121
11	11
	1

Hence, 8712 = 2 × 2 × 2 × 3 × 3 × 11 × 11.

(vi) 13500

2	13500
2	6750
3	3375
3	1125
3	375
5	125
5	25
5	5
	1

Hence, 13500 = 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5.

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State whether the following statements are true (T) or false (F):
(i) If a number is divisible by 4, it must be divisible by 8.
(ii) If a number is divisible by 3, it must be divisible by 9.
(iii) If a number is divisible by 9, it must be divisible by 3.
(iv) If a number is divisible by 9 and 10 both, it must be divisible by 90.
(v) If a number divides the sum of two numbers, then it must divide the two numbers separately.
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(vii) If a number is divisible by 6 and 15 both, it must be divisible by 90.
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