What is the Greatest Common Factor of 29712 and 29729?

Greatest common factor (GCF) of 29712 and 29729 is 1.

GCF(29712,29729) = 1

We will now calculate the prime factors of 29712 and 29729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29712 and 29729.

How to find the GCF of 29712 and 29729?

We will first find the prime factorization of 29712 and 29729. After we will calculate the factors of 29712 and 29729 and find the biggest common factor number .

Step-1: Prime Factorization of 29712

Prime factors of 29712 are 2, 3, 619. Prime factorization of 29712 in exponential form is:

29712 = 2⁴ × 3¹ × 619¹

Step-2: Prime Factorization of 29729

Prime factors of 29729 are 7, 31, 137. Prime factorization of 29729 in exponential form is:

29729 = 7¹ × 31¹ × 137¹

Step-3: Factors of 29712

List of positive integer factors of 29712 that divides 29712 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 619, 1238, 1857, 2476, 3714, 4952, 7428, 9904, 14856

Step-4: Factors of 29729

List of positive integer factors of 29729 that divides 29712 without a remainder.

1, 7, 31, 137, 217, 959, 4247

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29712 and 29729. The biggest common factor number is the GCF number.
So the greatest common factor 29712 and 29729 is 1.

Also check out the Least Common Multiple of 29712 and 29729