What is the Greatest Common Factor of 31584 and 31602?

Greatest common factor (GCF) of 31584 and 31602 is 6.

GCF(31584,31602) = 6

We will now calculate the prime factors of 31584 and 31602, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31584 and 31602.

How to find the GCF of 31584 and 31602?

We will first find the prime factorization of 31584 and 31602. After we will calculate the factors of 31584 and 31602 and find the biggest common factor number .

Step-1: Prime Factorization of 31584

Prime factors of 31584 are 2, 3, 7, 47. Prime factorization of 31584 in exponential form is:

31584 = 2⁵ × 3¹ × 7¹ × 47¹

Step-2: Prime Factorization of 31602

Prime factors of 31602 are 2, 3, 23, 229. Prime factorization of 31602 in exponential form is:

31602 = 2¹ × 3¹ × 23¹ × 229¹

Step-3: Factors of 31584

List of positive integer factors of 31584 that divides 31584 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 47, 48, 56, 84, 94, 96, 112, 141, 168, 188, 224, 282, 329, 336, 376, 564, 658, 672, 752, 987, 1128, 1316, 1504, 1974, 2256, 2632, 3948, 4512, 5264, 7896, 10528, 15792

Step-4: Factors of 31602

List of positive integer factors of 31602 that divides 31584 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138, 229, 458, 687, 1374, 5267, 10534, 15801

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31584 and 31602. The biggest common factor number is the GCF number.
So the greatest common factor 31584 and 31602 is 6.

Also check out the Least Common Multiple of 31584 and 31602