What is the Greatest Common Factor of 51744 and 51762?

Greatest common factor (GCF) of 51744 and 51762 is 6.

GCF(51744,51762) = 6

We will now calculate the prime factors of 51744 and 51762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51744 and 51762.

How to find the GCF of 51744 and 51762?

We will first find the prime factorization of 51744 and 51762. After we will calculate the factors of 51744 and 51762 and find the biggest common factor number .

Step-1: Prime Factorization of 51744

Prime factors of 51744 are 2, 3, 7, 11. Prime factorization of 51744 in exponential form is:

51744 = 2⁵ × 3¹ × 7² × 11¹

Step-2: Prime Factorization of 51762

Prime factors of 51762 are 2, 3, 8627. Prime factorization of 51762 in exponential form is:

51762 = 2¹ × 3¹ × 8627¹

Step-3: Factors of 51744

List of positive integer factors of 51744 that divides 51744 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 32, 33, 42, 44, 48, 49, 56, 66, 77, 84, 88, 96, 98, 112, 132, 147, 154, 168, 176, 196, 224, 231, 264, 294, 308, 336, 352, 392, 462, 528, 539, 588, 616, 672, 784, 924, 1056, 1078, 1176, 1232, 1568, 1617, 1848, 2156, 2352, 2464, 3234, 3696, 4312, 4704, 6468, 7392, 8624, 12936, 17248, 25872

Step-4: Factors of 51762

List of positive integer factors of 51762 that divides 51744 without a remainder.

1, 2, 3, 6, 8627, 17254, 25881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51744 and 51762. The biggest common factor number is the GCF number.
So the greatest common factor 51744 and 51762 is 6.

Also check out the Least Common Multiple of 51744 and 51762