What is the Greatest Common Factor of 210 and 220?

Greatest common factor (GCF) of 210 and 220 is 10.

GCF(210,220) = 10

We will now calculate the prime factors of 210 and 220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 210 and 220.

How to find the GCF of 210 and 220?

We will first find the prime factorization of 210 and 220. After we will calculate the factors of 210 and 220 and find the biggest common factor number .

Step-1: Prime Factorization of 210

Prime factors of 210 are 2, 3, 5, 7. Prime factorization of 210 in exponential form is:

210 = 2¹ × 3¹ × 5¹ × 7¹

Step-2: Prime Factorization of 220

Prime factors of 220 are 2, 5, 11. Prime factorization of 220 in exponential form is:

220 = 2² × 5¹ × 11¹

Step-3: Factors of 210

List of positive integer factors of 210 that divides 210 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105

Step-4: Factors of 220

List of positive integer factors of 220 that divides 210 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 210 and 220. The biggest common factor number is the GCF number.
So the greatest common factor 210 and 220 is 10.

Also check out the Least Common Multiple of 210 and 220