What is the Greatest Common Factor of 32960 and 32970?

Greatest common factor (GCF) of 32960 and 32970 is 10.

GCF(32960,32970) = 10

We will now calculate the prime factors of 32960 and 32970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32960 and 32970.

How to find the GCF of 32960 and 32970?

We will first find the prime factorization of 32960 and 32970. After we will calculate the factors of 32960 and 32970 and find the biggest common factor number .

Step-1: Prime Factorization of 32960

Prime factors of 32960 are 2, 5, 103. Prime factorization of 32960 in exponential form is:

32960 = 2⁶ × 5¹ × 103¹

Step-2: 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-3: Factors of 32960

List of positive integer factors of 32960 that divides 32960 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 103, 160, 206, 320, 412, 515, 824, 1030, 1648, 2060, 3296, 4120, 6592, 8240, 16480

Step-4: Factors of 32970

List of positive integer factors of 32970 that divides 32960 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32960 and 32970. The biggest common factor number is the GCF number.
So the greatest common factor 32960 and 32970 is 10.

Also check out the Least Common Multiple of 32960 and 32970