What is the Greatest Common Factor of 29900 and 29920?

Greatest common factor (GCF) of 29900 and 29920 is 20.

GCF(29900,29920) = 20

We will now calculate the prime factors of 29900 and 29920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29900 and 29920.

How to find the GCF of 29900 and 29920?

We will first find the prime factorization of 29900 and 29920. After we will calculate the factors of 29900 and 29920 and find the biggest common factor number .

Step-1: Prime Factorization of 29900

Prime factors of 29900 are 2, 5, 13, 23. Prime factorization of 29900 in exponential form is:

29900 = 2² × 5² × 13¹ × 23¹

Step-2: Prime Factorization of 29920

Prime factors of 29920 are 2, 5, 11, 17. Prime factorization of 29920 in exponential form is:

29920 = 2⁵ × 5¹ × 11¹ × 17¹

Step-3: Factors of 29900

List of positive integer factors of 29900 that divides 29900 without a remainder.

1, 2, 4, 5, 10, 13, 20, 23, 25, 26, 46, 50, 52, 65, 92, 100, 115, 130, 230, 260, 299, 325, 460, 575, 598, 650, 1150, 1196, 1300, 1495, 2300, 2990, 5980, 7475, 14950

Step-4: Factors of 29920

List of positive integer factors of 29920 that divides 29900 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 17, 20, 22, 32, 34, 40, 44, 55, 68, 80, 85, 88, 110, 136, 160, 170, 176, 187, 220, 272, 340, 352, 374, 440, 544, 680, 748, 880, 935, 1360, 1496, 1760, 1870, 2720, 2992, 3740, 5984, 7480, 14960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29900 and 29920. The biggest common factor number is the GCF number.
So the greatest common factor 29900 and 29920 is 20.

Also check out the Least Common Multiple of 29900 and 29920