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If you know the prime factorization of a number, you can find out the total number of factors.

Example: 210

2^1 x 3^1 x 5^1 x 7^1 = 210

Add one to the exponents and multiply them.

2 x 2 x 2 x 2 = 16, the total number of factors.

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The factor pairs are all the factors of the number, just listed in pairs.

Q: How can finding factor pairs help with finding all of the factors number?

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The difference is between factor pairs and distinct factors. With square numbers, one of the factor pairs will be the same number twice. When listing the distinct factors, that number is only listed once.

6

1,24

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.

Its only factors are itself and one because 71 is a prime number

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The difference is between factor pairs and distinct factors. With square numbers, one of the factor pairs will be the same number twice. When listing the distinct factors, that number is only listed once.

A square number has an odd number of factors, but a number with an odd number of factor pairs is nothing special.

Factor pairs are just the factors of a number listed in a different way. The factors of 20 are 1, 2, 4, 5, 10, 20 The factor pairs of 20 are (20,1)(10,2)(5,4)

The factor pairs of 21 are:1, 213, 7Therefore, the number 21 has two pairs of positive integer factors.

60 has 6 factor pairs.

Factors can be listed as factor pairs. With square numbers, one of those pairs will be the same number twice. When written as a list, only one of them will be used, leaving an odd number of factors.

Factors come in pairs. If you know one factor, divide it into the number. The answer will be another factor.

For every factor of a number, there is another factor that results when you divide the first factor into the number. Factors can be listed in pairs. Since 9 x 4 = 36, (9,4) is a factor pair of 36.

1 and 13. It is a prime number, so those are its only factor.

As I understand it, the number of factor pairs is equal to the number of rectangles.

The number 4 has two factor pairs. 1 x 4 and 2 x 2

Factors are numbers you can multiply together to get another number. The factor pairs are: (1, 52) (2, 26) (4, 13)