What is the Greatest Common Factor of 32970 and 32984?

Greatest common factor (GCF) of 32970 and 32984 is 14.

GCF(32970,32984) = 14

We will now calculate the prime factors of 32970 and 32984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32970 and 32984.

How to find the GCF of 32970 and 32984?

We will first find the prime factorization of 32970 and 32984. After we will calculate the factors of 32970 and 32984 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 32984

Prime factors of 32984 are 2, 7, 19, 31. Prime factorization of 32984 in exponential form is:

32984 = 2³ × 7¹ × 19¹ × 31¹

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 32984

List of positive integer factors of 32984 that divides 32970 without a remainder.

1, 2, 4, 7, 8, 14, 19, 28, 31, 38, 56, 62, 76, 124, 133, 152, 217, 248, 266, 434, 532, 589, 868, 1064, 1178, 1736, 2356, 4123, 4712, 8246, 16492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32970 and 32984. The biggest common factor number is the GCF number.
So the greatest common factor 32970 and 32984 is 14.

Also check out the Least Common Multiple of 32970 and 32984