What is the Greatest Common Factor of 29745 and 29760?

Greatest common factor (GCF) of 29745 and 29760 is 15.

GCF(29745,29760) = 15

We will now calculate the prime factors of 29745 and 29760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29745 and 29760.

How to find the GCF of 29745 and 29760?

We will first find the prime factorization of 29745 and 29760. After we will calculate the factors of 29745 and 29760 and find the biggest common factor number .

Step-1: Prime Factorization of 29745

Prime factors of 29745 are 3, 5, 661. Prime factorization of 29745 in exponential form is:

29745 = 3² × 5¹ × 661¹

Step-2: Prime Factorization of 29760

Prime factors of 29760 are 2, 3, 5, 31. Prime factorization of 29760 in exponential form is:

29760 = 2⁶ × 3¹ × 5¹ × 31¹

Step-3: Factors of 29745

List of positive integer factors of 29745 that divides 29745 without a remainder.

1, 3, 5, 9, 15, 45, 661, 1983, 3305, 5949, 9915

Step-4: Factors of 29760

List of positive integer factors of 29760 that divides 29745 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 64, 80, 93, 96, 120, 124, 155, 160, 186, 192, 240, 248, 310, 320, 372, 465, 480, 496, 620, 744, 930, 960, 992, 1240, 1488, 1860, 1984, 2480, 2976, 3720, 4960, 5952, 7440, 9920, 14880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29745 and 29760. The biggest common factor number is the GCF number.
So the greatest common factor 29745 and 29760 is 15.

Also check out the Least Common Multiple of 29745 and 29760