What is the Greatest Common Factor of 32970 and 32980?

Greatest common factor (GCF) of 32970 and 32980 is 10.

GCF(32970,32980) = 10

We will now calculate the prime factors of 32970 and 32980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32970 and 32980.

How to find the GCF of 32970 and 32980?

We will first find the prime factorization of 32970 and 32980. After we will calculate the factors of 32970 and 32980 and find the biggest common factor number .

Step-1: Prime Factorization of 32970

Prime factors of 32970 are 2, 3, 5, 7, 157. Prime factorization of 32970 in exponential form is:

32970 = 2¹ × 3¹ × 5¹ × 7¹ × 157¹

Step-2: Prime Factorization of 32980

Prime factors of 32980 are 2, 5, 17, 97. Prime factorization of 32980 in exponential form is:

32980 = 2² × 5¹ × 17¹ × 97¹

Step-3: Factors of 32970

List of positive integer factors of 32970 that divides 32970 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 157, 210, 314, 471, 785, 942, 1099, 1570, 2198, 2355, 3297, 4710, 5495, 6594, 10990, 16485

Step-4: Factors of 32980

List of positive integer factors of 32980 that divides 32970 without a remainder.

1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 97, 170, 194, 340, 388, 485, 970, 1649, 1940, 3298, 6596, 8245, 16490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32970 and 32980. The biggest common factor number is the GCF number.
So the greatest common factor 32970 and 32980 is 10.

Also check out the Least Common Multiple of 32970 and 32980