What is the Greatest Common Factor of 210 and 217?

Greatest common factor (GCF) of 210 and 217 is 7.

GCF(210,217) = 7

We will now calculate the prime factors of 210 and 217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 210 and 217.

How to find the GCF of 210 and 217?

We will first find the prime factorization of 210 and 217. After we will calculate the factors of 210 and 217 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 217

Prime factors of 217 are 7, 31. Prime factorization of 217 in exponential form is:

217 = 7¹ × 31¹

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 217

List of positive integer factors of 217 that divides 210 without a remainder.

1, 7, 31

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 210 and 217. The biggest common factor number is the GCF number.
So the greatest common factor 210 and 217 is 7.

Also check out the Least Common Multiple of 210 and 217