What is the Greatest Common Factor of 29729 and 29736?

Greatest common factor (GCF) of 29729 and 29736 is 7.

GCF(29729,29736) = 7

We will now calculate the prime factors of 29729 and 29736, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29729 and 29736.

How to find the GCF of 29729 and 29736?

We will first find the prime factorization of 29729 and 29736. After we will calculate the factors of 29729 and 29736 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 29736

Prime factors of 29736 are 2, 3, 7, 59. Prime factorization of 29736 in exponential form is:

29736 = 2³ × 3² × 7¹ × 59¹

Step-3: Factors of 29729

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

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

Step-4: Factors of 29736

List of positive integer factors of 29736 that divides 29729 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 59, 63, 72, 84, 118, 126, 168, 177, 236, 252, 354, 413, 472, 504, 531, 708, 826, 1062, 1239, 1416, 1652, 2124, 2478, 3304, 3717, 4248, 4956, 7434, 9912, 14868

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29729 and 29736. The biggest common factor number is the GCF number.
So the greatest common factor 29729 and 29736 is 7.

Also check out the Least Common Multiple of 29729 and 29736