Q:

What is the GCF of 70 and 90?

Accepted Solution

A:
Solution: The GCF of 70 and 90 is 10 Methods How to find the GCF of 70 and 90 using Prime Factorization One way to find the GCF of 70 and 90 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 90? 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 90: 2 1 × 3 2 × 5 1 2^1 × 3^2 × 5^1 2 1 × 3 2 × 5 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 90 by multiplying all the matching prime factors to get a GCF of 70 and 90 as 100: Thus, the GCF of 70 and 90 is: 100 How to Find the GCF of 70 and 90 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 70 and 90 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 90: Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 5, 10. Since 10 is the largest of these common factors, the GCF of 70 and 90 would be 10. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 12 and 101? What is the GCF of 79 and 46? What is the GCF of 8 and 34? What is the GCF of 6 and 38? What is the GCF of 136 and 148?