Solution: The GCF of 70 and 105 is 35
Methods
How to find the GCF of 70 and 105 using Prime Factorization
One way to find the GCF of 70 and 105 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 70?
What are the Factors of 105?
Here is the prime factorization of 70:
2
1
×
5
1
×
7
1
2^1 × 5^1 × 7^1
2 1 × 5 1 × 7 1
And this is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 1 × 7 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 70 and 105 by multiplying all the matching prime factors to get a GCF of 70 and 105 as 1225:
Thus, the GCF of 70 and 105 is: 1225
How to Find the GCF of 70 and 105 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 70 and 105 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 70 and 105:
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
When you compare the two lists of factors, you can see that the common factor(s) are 1, 5, 7, 35. Since 35 is the largest of these common factors, the GCF of 70 and 105 would be 35.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 141 and 69?
What is the GCF of 132 and 145?
What is the GCF of 41 and 124?
What is the GCF of 18 and 37?
What is the GCF of 100 and 113?