# Prime Factorization of 36 and 70

Number 1Number 2(Optional) Enter Number 3

Using the Prime Factorization Method, calculate the GCF of (36,70)

Now, show the prime factorization (factor tree) for 36 by expressing it as the product of ALL prime numbers.
36 = 2 x 18 <--- 2 is a prime number

Next step is to reduce 18 to the product of prime numbers:
18 = 3 x 6 <--- 3 is a prime number

Next step is to reduce 6 to the product of prime numbers:
6 = 2 x 3 <--- 2 is a prime number

Next step is to reduce 3 to the product of prime numbers:
Our prime factorization (factor tree) is as follows:
The prime factorization for 36 is 2 x 2 x 3 x 3

Now, show the prime factorization (factor tree) for 70 by expressing it as the product of ALL prime numbers.
70 = 2 x 35 <--- 2 is a prime number

Next step is to reduce 35 to the product of prime numbers:
35 = 5 x 7 <--- 5 is a prime number

Next step is to reduce 7 to the product of prime numbers:
Our prime factorization (factor tree) is as follows:
The prime factorization for 70 is 2 x 5 x 7

Find Matching Primes from each factorization in red:
Prime factorization for 36 = 2 x 2 x 3 x 3
Prime factorization for 70 = 2 x 5 x 7

Based on this our GCF is:
GCF of (36,70) = 2