What is the Greatest Common Factor of 59976 and 59984?

Greatest common factor (GCF) of 59976 and 59984 is 8.

GCF(59976,59984) = 8

We will now calculate the prime factors of 59976 and 59984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59976 and 59984.

How to find the GCF of 59976 and 59984?

We will first find the prime factorization of 59976 and 59984. After we will calculate the factors of 59976 and 59984 and find the biggest common factor number .

Step-1: Prime Factorization of 59976

Prime factors of 59976 are 2, 3, 7, 17. Prime factorization of 59976 in exponential form is:

59976 = 2³ × 3² × 7² × 17¹

Step-2: Prime Factorization of 59984

Prime factors of 59984 are 2, 23, 163. Prime factorization of 59984 in exponential form is:

59984 = 2⁴ × 23¹ × 163¹

Step-3: Factors of 59976

List of positive integer factors of 59976 that divides 59976 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 17, 18, 21, 24, 28, 34, 36, 42, 49, 51, 56, 63, 68, 72, 84, 98, 102, 119, 126, 136, 147, 153, 168, 196, 204, 238, 252, 294, 306, 357, 392, 408, 441, 476, 504, 588, 612, 714, 833, 882, 952, 1071, 1176, 1224, 1428, 1666, 1764, 2142, 2499, 2856, 3332, 3528, 4284, 4998, 6664, 7497, 8568, 9996, 14994, 19992, 29988

Step-4: Factors of 59984

List of positive integer factors of 59984 that divides 59976 without a remainder.

1, 2, 4, 8, 16, 23, 46, 92, 163, 184, 326, 368, 652, 1304, 2608, 3749, 7498, 14996, 29992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59976 and 59984. The biggest common factor number is the GCF number.
So the greatest common factor 59976 and 59984 is 8.

Also check out the Least Common Multiple of 59976 and 59984