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All non-zero numbers have factors. Some factors are prime, some are composite. The set of prime factors is a subset of the set of total factors.

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Q: What is connection between prime factors and total factors?

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Two distinct prime factors, six total prime factors.

Three distinct prime factors, eight total.

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If all the factors are prime numbers and they total the original number, you have found them all. All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime. 2 x 3 x 5 x 7 = 210 That's the prime factorization of 210.

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Two distinct prime factors, six total prime factors.

A multiplication sentence where prime factors total a given composite number is known as a prime factorization.

The prime factorization of 42 is 2x3x7. The prime factors are 2, 3, and 7. There are eight total factors of 42: 1, 2, 3, 6, 7, 14, 21, and 42.

All numbers have factors. Some factors are prime numbers, some are composite numbers, one is neither. When finding the factors of a number, you find all the factors. The prime factorization is a multiplication string of just prime factors that will total the given number.

Out of four total factors, 85 has two prime factors: 5 and 17.

36 as a product of its prime factors is 2 x 2 x 3 x 3. Their total is 10. 36 as a product of factors that total 13 is 4 x 9

Three distinct prime factors, eight total.

It has three prime factors, but not factors in total.

In order to be relatively prime to 12, it can't have the factors 2 or 3. Let's try 5^2 x 7^2 x 11. 13475 has three prime factors, 18 divisors, and is relatively prime to 12.

The best way to get lots of factors is to ensure that no prime factors occur more than once. If this is the case, and there are n prime factors altogether, then there will be 2n factors in total. * In fact you can get more factors by repeating some of the small prime factors. For example, 210 = 2 x 3 x 5 x 7 has 16 factors, but 180 = 22 x 32 x 5 has 18 factors. * There is more info on my website at www.dansmath.com about supercomposite numbers and their prime factorization structure.

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