Question

There are nine square number less than 100. Which one has the largest factors?

Answer 1

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The square numbers under 100 are 1, 4, 9, 16, 25, 36, 49, 64, and 81.

1 obviously only factors to 1 × 1.

4, 9, 25, and 49 are square of prime numbers. If we call the original number n and the root p (for prime) each of them can only be factored as 1 × n or p × p. example: 1 × 4 , 2 × 2 .We can eliminate those.

16 and 81 are not only squares, but the fourth power of a prime (2 and 3) respectively. They can be factored as 1 × n, (p³) × p, or (p² × p²). Example: 1 × 16, 8 × 2, or 4 × 4.

But 36 is 2*2*3*3 as it’s prime factoring. This allows us to find more combinations of factors :

1 × 36 , 2 × 18 , 4 × 9 , 12 × 3 , or 6 × 6.

Answer 2

Answer:

I hope

factor of 81 - 3, 9, 27 ( 3 factor)