Write the prime factorization of each number in exponential notation.

1. 4,725

2. 65,520

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

Divisibility rules of use are