What is the Greatest Common Factor of 210 and 224?

Greatest common factor (GCF) of 210 and 224 is 14.

GCF(210,224) = 14

We will now calculate the prime factors of 210 and 224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 210 and 224.

How to find the GCF of 210 and 224?

We will first find the prime factorization of 210 and 224. After we will calculate the factors of 210 and 224 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 224

Prime factors of 224 are 2, 7. Prime factorization of 224 in exponential form is:

224 = 2⁵ × 7¹

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 224

List of positive integer factors of 224 that divides 210 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 210 and 224. The biggest common factor number is the GCF number.
So the greatest common factor 210 and 224 is 14.

Also check out the Least Common Multiple of 210 and 224