2 x 2 = 4
2 x 3 = 6
2 x 2 x 2 = 8
3 x 3 = 9
2 x 5 = 10
2 x 2 x 3 = 12
2 x 7 = 14
3 x 5 = 15
2 x 2 x 2 x 2 = 16
2 x 3 x 3 = 18
2 x 2 x 5 = 20
3 x 7 = 21
2 x 11 = 22
2 x 2 x 2 x 3 = 24
5 x 5 = 25
2 x 13 = 26
3 x 3 x 3 = 27
2 x 2 x 7 = 28
2 x 3 x 5 = 30
2 x 2 x 2 x 2 x 2 = 32
3 x 11 = 33
2 x 17 = 34
5 x 7 = 35
2 x 2 x 3 x 3 = 36
2 x 19 = 38
3 x 13 = 39
2 x 2 x 2 x 5 = 40
2 x 3 x 7 = 42
2 x 2 x 11 = 44
3 x 3 x 5 = 45
2 x 23 = 46
2 x 2 x 2 x 2 x 3 = 48
7 x 7 = 49
2 x 5 x 5 = 50
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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.
The prime factorization of the number 33 is: 3 x 11
By factoring them. Prime numbers have only two factors. Composite numbers have three or more.
All composite numbers can be expressed as the product of prime numbers. This is accomplished by dividing the original number by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 30 30 Divide by two. 15,2 Divide by three. 5,3,2 Stop. All the factors are prime. 2 x 3 x 5 = 30 That's the prime factorization of 30.
Writing down all the factors of both numbers requires too much time so it is not a good idea to find solution by writing each factor of both numbers. Method of prime factorization is one of the good methods to find GCF. Prime factorization is like breaking a number into other numbers, prime numbers, and this factorization is unique. Prime factorization is like a blueprint for numbers. Prime factorization of 1820 = 22 x 5 x 7 x 13 Prime factorization of 637 = 7 x 7 x 13 7, 13 and 7x13 are common in the prime factorization of both numbers, but 7x13 is the greatest among these numbers. So, 7x13 = 91 is the GCF of 1820 and 637.