What is the Greatest Common Factor of 29744 and 29757?

Greatest common factor (GCF) of 29744 and 29757 is 13.

GCF(29744,29757) = 13

We will now calculate the prime factors of 29744 and 29757, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29744 and 29757.

How to find the GCF of 29744 and 29757?

We will first find the prime factorization of 29744 and 29757. After we will calculate the factors of 29744 and 29757 and find the biggest common factor number .

Step-1: Prime Factorization of 29744

Prime factors of 29744 are 2, 11, 13. Prime factorization of 29744 in exponential form is:

29744 = 2⁴ × 11¹ × 13²

Step-2: Prime Factorization of 29757

Prime factors of 29757 are 3, 7, 13, 109. Prime factorization of 29757 in exponential form is:

29757 = 3¹ × 7¹ × 13¹ × 109¹

Step-3: Factors of 29744

List of positive integer factors of 29744 that divides 29744 without a remainder.

1, 2, 4, 8, 11, 13, 16, 22, 26, 44, 52, 88, 104, 143, 169, 176, 208, 286, 338, 572, 676, 1144, 1352, 1859, 2288, 2704, 3718, 7436, 14872

Step-4: Factors of 29757

List of positive integer factors of 29757 that divides 29744 without a remainder.

1, 3, 7, 13, 21, 39, 91, 109, 273, 327, 763, 1417, 2289, 4251, 9919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29744 and 29757. The biggest common factor number is the GCF number.
So the greatest common factor 29744 and 29757 is 13.

Also check out the Least Common Multiple of 29744 and 29757