What is the Greatest Common Factor of 29744 and 29762?

Greatest common factor (GCF) of 29744 and 29762 is 2.

GCF(29744,29762) = 2

We will now calculate the prime factors of 29744 and 29762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29744 and 29762.

How to find the GCF of 29744 and 29762?

We will first find the prime factorization of 29744 and 29762. After we will calculate the factors of 29744 and 29762 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 29762

Prime factors of 29762 are 2, 23, 647. Prime factorization of 29762 in exponential form is:

29762 = 2¹ × 23¹ × 647¹

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 29762

List of positive integer factors of 29762 that divides 29744 without a remainder.

1, 2, 23, 46, 647, 1294, 14881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29744 and 29762. The biggest common factor number is the GCF number.
So the greatest common factor 29744 and 29762 is 2.

Also check out the Least Common Multiple of 29744 and 29762