What is the Greatest Common Factor of 29625 and 29640?

Greatest common factor (GCF) of 29625 and 29640 is 15.

GCF(29625,29640) = 15

We will now calculate the prime factors of 29625 and 29640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29625 and 29640.

How to find the GCF of 29625 and 29640?

We will first find the prime factorization of 29625 and 29640. After we will calculate the factors of 29625 and 29640 and find the biggest common factor number .

Step-1: Prime Factorization of 29625

Prime factors of 29625 are 3, 5, 79. Prime factorization of 29625 in exponential form is:

29625 = 3¹ × 5³ × 79¹

Step-2: Prime Factorization of 29640

Prime factors of 29640 are 2, 3, 5, 13, 19. Prime factorization of 29640 in exponential form is:

29640 = 2³ × 3¹ × 5¹ × 13¹ × 19¹

Step-3: Factors of 29625

List of positive integer factors of 29625 that divides 29625 without a remainder.

1, 3, 5, 15, 25, 75, 79, 125, 237, 375, 395, 1185, 1975, 5925, 9875

Step-4: Factors of 29640

List of positive integer factors of 29640 that divides 29625 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 19, 20, 24, 26, 30, 38, 39, 40, 52, 57, 60, 65, 76, 78, 95, 104, 114, 120, 130, 152, 156, 190, 195, 228, 247, 260, 285, 312, 380, 390, 456, 494, 520, 570, 741, 760, 780, 988, 1140, 1235, 1482, 1560, 1976, 2280, 2470, 2964, 3705, 4940, 5928, 7410, 9880, 14820

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29625 and 29640. The biggest common factor number is the GCF number.
So the greatest common factor 29625 and 29640 is 15.

Also check out the Least Common Multiple of 29625 and 29640