###### Asked in Factoring and Multiples

Factoring and Multiples

# How does findingthe prime factorization of a group of numbers help you to find the greatest common factor?

## Answer

###### Wiki User

###### March 02, 2013 6:28PM

Once you have the prime factorizations, it's easy to spot the factors they have in common.

Example: 30 and 42

**2 x 3** x 5 = 30

**2 x 3** x 7 = 42

2 x 3 = 6, the GCF

## Related Questions

###### Asked in Factoring and Multiples

### What is the greatest common factor of 132 and 150?

The answer is 6.You need to do a prime factorization of the 2
numbers first. Then compare the 2 numbers and see what the greatest
number they have in common is in the factorization of them. Next
times what they have in common and there is your answer. The
factorization of 132=11x3x2x2 The factorization of 150=5x5x3x2
There is a 2 and a 3 in each, so you multiply them both and you get
6.

###### Asked in Factoring and Multiples

### What is the prime factorization and the greatest common factor of 2456?

The prime factorization of 2456 is 2 x 2 x 2 x 307.
There is not a greatest common factor. To have a greatest common
factor, you need two or more numbers. A common factor is a factor
that two or more number have in common.
However, the prime factorization of all the numbers will help
you find the greatest common factor. The greatest common factor
will be the prime factors they have in common multiplied
together.
Examples:
The prime factorization of 36 is 2 x 2 x 3 x 3. The prime
factors it has in common with 2456 are 2 and 2, so the greatest
common factor is 2 x 2 = 4.
The prime factorization of 921 is 3 x 307. The prime factors
that it has in common with 2456 is 307, so the greatest common
factor is 307.

###### Asked in Factoring and Multiples

### How do you find the greatest common factor of 30135 using prime factorization?

You do not. To have a greatest common factor, you need two or
more numbers. A common factor is a factor that two or more number
have in common.
However, the prime factorization of all the numbers will help
you find the greatest common factor. The greatest common factor
will be the prime factors they have in common multiplied
together.
Example:
The prime factorization of 30135 is 3 x 5 x 7 x 7 x 41.
The prime factorization of 98 is 2 x 7 x 7.
The prime factors they have in common are 7 and 7, so the
greatest common factor is 7 x 7 = 49.

###### Asked in Factoring and Multiples

### What is the pime factorization and gcf of 12?

The prime factorization of 12 is: 2 x 2 x 3 = 12
However, there cannot be a greatest common factor (GCF) of just
one number. To be common there need to be at least two numbers. If
you find all the factors of two or more numbers, and you
find some factors are the same ("common"), then the largest of
those common factors is the Greatest Common Factor.

###### Asked in Factoring and Multiples

### How do you find the greatest common factor of 45 using prime factorization?

You do not. To have a greatest common factor, you need two or
more numbers. A common factor is a factor that two or more number
have in common.
However, the prime factorization of all the numbers will help
you find the greatest common factor. The greatest common factor
will be the prime factors they have in common multiplied
together.
Example:
The prime factors of 45 are 3, 3, and 5.
The prime factors of 60 are 2, 2, 3, and 5.
The common prime factors are 3 and 5, so the greatest common
factor is 3 x 5 = 15.

Load More