What is the Greatest Common Factor of 51744 and 51758?

Greatest common factor (GCF) of 51744 and 51758 is 14.

GCF(51744,51758) = 14

We will now calculate the prime factors of 51744 and 51758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51744 and 51758.

How to find the GCF of 51744 and 51758?

We will first find the prime factorization of 51744 and 51758. After we will calculate the factors of 51744 and 51758 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 51758

Prime factors of 51758 are 2, 7, 3697. Prime factorization of 51758 in exponential form is:

51758 = 2¹ × 7¹ × 3697¹

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 51758

List of positive integer factors of 51758 that divides 51744 without a remainder.

1, 2, 7, 14, 3697, 7394, 25879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51744 and 51758. The biggest common factor number is the GCF number.
So the greatest common factor 51744 and 51758 is 14.

Also check out the Least Common Multiple of 51744 and 51758