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Q: Why the longest string of prime factors for 30 is 1x2x1x3x1x5?

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The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.

When all of the numbers are prime.

You will know because all of the numbers are prime.

2

It's a pretty short string. 29 is prime, its only factors are 1 and itself.

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Because 1 isn't prime.

The prime factorization.

The prime factorization.

2x3x5

When all of the factors are prime. The longest factor string is the prime factorization.

When all the factors are prime.

The longest string of prime factors for 30 is 2 x 3 x 5 because there isn't a prime factor string that's longer.

Find the prime factors first.

The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.

the longest string of prime factor for 30 is 2 x 3 x 5

For composite numbers, only one string of factors is the longest; the prime factorization.

All of the factors are prime.