What is the Greatest Common Factor of 49980 and 49984?

Greatest common factor (GCF) of 49980 and 49984 is 4.

GCF(49980,49984) = 4

We will now calculate the prime factors of 49980 and 49984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49980 and 49984.

How to find the GCF of 49980 and 49984?

We will first find the prime factorization of 49980 and 49984. After we will calculate the factors of 49980 and 49984 and find the biggest common factor number .

Step-1: Prime Factorization of 49980

Prime factors of 49980 are 2, 3, 5, 7, 17. Prime factorization of 49980 in exponential form is:

49980 = 2² × 3¹ × 5¹ × 7² × 17¹

Step-2: Prime Factorization of 49984

Prime factors of 49984 are 2, 11, 71. Prime factorization of 49984 in exponential form is:

49984 = 2⁶ × 11¹ × 71¹

Step-3: Factors of 49980

List of positive integer factors of 49980 that divides 49980 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 49, 51, 60, 68, 70, 84, 85, 98, 102, 105, 119, 140, 147, 170, 196, 204, 210, 238, 245, 255, 294, 340, 357, 420, 476, 490, 510, 588, 595, 714, 735, 833, 980, 1020, 1190, 1428, 1470, 1666, 1785, 2380, 2499, 2940, 3332, 3570, 4165, 4998, 7140, 8330, 9996, 12495, 16660, 24990

Step-4: Factors of 49984

List of positive integer factors of 49984 that divides 49980 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 71, 88, 142, 176, 284, 352, 568, 704, 781, 1136, 1562, 2272, 3124, 4544, 6248, 12496, 24992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49980 and 49984. The biggest common factor number is the GCF number.
So the greatest common factor 49980 and 49984 is 4.

Also check out the Least Common Multiple of 49980 and 49984