What is the Greatest Common Factor of 29875 and 29880?

Greatest common factor (GCF) of 29875 and 29880 is 5.

GCF(29875,29880) = 5

We will now calculate the prime factors of 29875 and 29880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29875 and 29880.

How to find the GCF of 29875 and 29880?

We will first find the prime factorization of 29875 and 29880. After we will calculate the factors of 29875 and 29880 and find the biggest common factor number .

Step-1: Prime Factorization of 29875

Prime factors of 29875 are 5, 239. Prime factorization of 29875 in exponential form is:

29875 = 5³ × 239¹

Step-2: Prime Factorization of 29880

Prime factors of 29880 are 2, 3, 5, 83. Prime factorization of 29880 in exponential form is:

29880 = 2³ × 3² × 5¹ × 83¹

Step-3: Factors of 29875

List of positive integer factors of 29875 that divides 29875 without a remainder.

1, 5, 25, 125, 239, 1195, 5975

Step-4: Factors of 29880

List of positive integer factors of 29880 that divides 29875 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 83, 90, 120, 166, 180, 249, 332, 360, 415, 498, 664, 747, 830, 996, 1245, 1494, 1660, 1992, 2490, 2988, 3320, 3735, 4980, 5976, 7470, 9960, 14940

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29875 and 29880. The biggest common factor number is the GCF number.
So the greatest common factor 29875 and 29880 is 5.

Also check out the Least Common Multiple of 29875 and 29880