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Perfect powers, divisibility and constrained prime factors
Free examples and worked answers. No account needed.
Practise the method.
Perfect powers, divisibility and constrained prime factors
Optional enrichment: Perfect powers, divisibility and constrained prime factors
Example 1
N=25×310. How many positive divisors of N are perfect squares?
Show worked answer
Answer: 18
- Square divisors use exponents 0,2, …, 4 for 2 and 0,2, …, 10 for 3.
- 3×6 choices.
Example 2
Two positive integers have HCF 2 and LCM 24. Their sum is 14. Find the larger integer.
Show worked answer
Answer: 8
- Their product is HCF ×LCM=48.
- With sum 14, the integers are 6 and 8;
- the larger is 8.
Example 3
N=25×312. How many positive divisors of N are perfect squares?
Show worked answer
Answer: 21
- Square divisors use exponents 0,2, …, 4 for 2 and 0,2, …, 12 for 3.
- 3×7 choices.
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