What is the Greatest Common Factor of 29715 and 29729?

Greatest common factor (GCF) of 29715 and 29729 is 7.

GCF(29715,29729) = 7

We will now calculate the prime factors of 29715 and 29729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29715 and 29729.

How to find the GCF of 29715 and 29729?

We will first find the prime factorization of 29715 and 29729. After we will calculate the factors of 29715 and 29729 and find the biggest common factor number .

Step-1: Prime Factorization of 29715

Prime factors of 29715 are 3, 5, 7, 283. Prime factorization of 29715 in exponential form is:

29715 = 3¹ × 5¹ × 7¹ × 283¹

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 29715

List of positive integer factors of 29715 that divides 29715 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 283, 849, 1415, 1981, 4245, 5943, 9905

Step-4: Factors of 29729

List of positive integer factors of 29729 that divides 29715 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29715 and 29729. The biggest common factor number is the GCF number.
So the greatest common factor 29715 and 29729 is 7.

Also check out the Least Common Multiple of 29715 and 29729