What is the Greatest Common Factor of 49296 and 49300?

Greatest common factor (GCF) of 49296 and 49300 is 4.

GCF(49296,49300) = 4

We will now calculate the prime factors of 49296 and 49300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49296 and 49300.

How to find the GCF of 49296 and 49300?

We will first find the prime factorization of 49296 and 49300. After we will calculate the factors of 49296 and 49300 and find the biggest common factor number .

Step-1: Prime Factorization of 49296

Prime factors of 49296 are 2, 3, 13, 79. Prime factorization of 49296 in exponential form is:

49296 = 2⁴ × 3¹ × 13¹ × 79¹

Step-2: 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-3: Factors of 49296

List of positive integer factors of 49296 that divides 49296 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 79, 104, 156, 158, 208, 237, 312, 316, 474, 624, 632, 948, 1027, 1264, 1896, 2054, 3081, 3792, 4108, 6162, 8216, 12324, 16432, 24648

Step-4: Factors of 49300

List of positive integer factors of 49300 that divides 49296 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49296 and 49300. The biggest common factor number is the GCF number.
So the greatest common factor 49296 and 49300 is 4.

Also check out the Least Common Multiple of 49296 and 49300