Answer:
- (3^3)(5^2)(7)
- (2^4)(3^2)(5)(7)(13)
Step-by-step explanation:
It is convenient to make use of divisibility rules as far as possible.
1. 4725 is obviously divisible by 25, so we have ...
4725 = 5^2 × 189
The sum of digits of 189 is divisible by 9, so that number is as well
4725 = 5^2 × 3^2 × 21
Your knowledge of multiplication tables tells you 21 = 3×7, so the prime factorization is ...
4725 = 3^3 × 5^2 × 7
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2. 65520 is apparently divisible by 20, so we have ...
65520 = 2^2 × 5 × 3276
3276 has a sum of digits divisible by 9, so it is divisible by 9.
65520 = 2^2 × 3^2 × 5 × 364
364 is apparently divisible by 4, so ...
65520 = 2^4 × 3^2 × 5 × 91
91 is divisible by 7, so the final prime factorization is ...
65520 = 2^4 × 3^2 × 5 × 7 × 13
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Divisibility rules of use are
- divisible by 2 if ones digit is even
- divisible by 3 if sum of digits is divisible by 3
- divisible by 5 is ones digit is 0 or 5
- divisible by 7 if the number Nx is such that N-2x is divisible by 7 (N is the number with the ones digit (x) removed) Here, 91 ⇒ 9-2·1 = 7 is divisible by 7.
- divisible by 9 if sum of digits is divisible by 9
