What is the Greatest Common Factor of 51730 and 51744?

Greatest common factor (GCF) of 51730 and 51744 is 14.

GCF(51730,51744) = 14

We will now calculate the prime factors of 51730 and 51744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51730 and 51744.

How to find the GCF of 51730 and 51744?

We will first find the prime factorization of 51730 and 51744. After we will calculate the factors of 51730 and 51744 and find the biggest common factor number .

Step-1: Prime Factorization of 51730

Prime factors of 51730 are 2, 5, 7, 739. Prime factorization of 51730 in exponential form is:

51730 = 2¹ × 5¹ × 7¹ × 739¹

Step-2: 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-3: Factors of 51730

List of positive integer factors of 51730 that divides 51730 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 739, 1478, 3695, 5173, 7390, 10346, 25865

Step-4: Factors of 51744

List of positive integer factors of 51744 that divides 51730 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51730 and 51744. The biggest common factor number is the GCF number.
So the greatest common factor 51730 and 51744 is 14.

Also check out the Least Common Multiple of 51730 and 51744