What is the Greatest Common Factor of 49300 and 49312?

Greatest common factor (GCF) of 49300 and 49312 is 4.

GCF(49300,49312) = 4

We will now calculate the prime factors of 49300 and 49312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49300 and 49312.

How to find the GCF of 49300 and 49312?

We will first find the prime factorization of 49300 and 49312. After we will calculate the factors of 49300 and 49312 and find the biggest common factor number .

Step-1: Prime Factorization of 49300

Prime factors of 49300 are 2, 5, 17, 29. Prime factorization of 49300 in exponential form is:

49300 = 2² × 5² × 17¹ × 29¹

Step-2: Prime Factorization of 49312

Prime factors of 49312 are 2, 23, 67. Prime factorization of 49312 in exponential form is:

49312 = 2⁵ × 23¹ × 67¹

Step-3: Factors of 49300

List of positive integer factors of 49300 that divides 49300 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 29, 34, 50, 58, 68, 85, 100, 116, 145, 170, 290, 340, 425, 493, 580, 725, 850, 986, 1450, 1700, 1972, 2465, 2900, 4930, 9860, 12325, 24650

Step-4: Factors of 49312

List of positive integer factors of 49312 that divides 49300 without a remainder.

1, 2, 4, 8, 16, 23, 32, 46, 67, 92, 134, 184, 268, 368, 536, 736, 1072, 1541, 2144, 3082, 6164, 12328, 24656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49300 and 49312. The biggest common factor number is the GCF number.
So the greatest common factor 49300 and 49312 is 4.

Also check out the Least Common Multiple of 49300 and 49312