Question

Must the prime factors of a composite number be less than the square root of the composite number?

Answer 1

Answer:

Step-by-step explanation:

Yes!

The square root of a number represents the "middle number" possible as a divisor of any given number.

All other factors will have one number above the square root and one number below the square root.

For example consider 80.

The prime factors are 2 * 2 * 2 * 2 * 5. The square root of 80 is about 9, so any factor of 80 must have all the primes under the square root or 1 above and 1 below.

10 * 8 is one such pair. 10 is above 9 and 8 is below it.

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I have read the comments made by others. I believe what they are saying is true, but I'm not interpreting the question the same way. I'm looking at these as pairs. The commenter is taking 1 prime at a time. It's a fair way to look at the question. You have to decide how you want to present your answer. You could go either way. That's the problem with some of these questions.