What is the Greatest Common Factor of 71904 and 71920?

Greatest common factor (GCF) of 71904 and 71920 is 16.

GCF(71904,71920) = 16

We will now calculate the prime factors of 71904 and 71920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71904 and 71920.

How to find the GCF of 71904 and 71920?

We will first find the prime factorization of 71904 and 71920. After we will calculate the factors of 71904 and 71920 and find the biggest common factor number .

Step-1: Prime Factorization of 71904

Prime factors of 71904 are 2, 3, 7, 107. Prime factorization of 71904 in exponential form is:

71904 = 2⁵ × 3¹ × 7¹ × 107¹

Step-2: Prime Factorization of 71920

Prime factors of 71920 are 2, 5, 29, 31. Prime factorization of 71920 in exponential form is:

71920 = 2⁴ × 5¹ × 29¹ × 31¹

Step-3: Factors of 71904

List of positive integer factors of 71904 that divides 71904 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 107, 112, 168, 214, 224, 321, 336, 428, 642, 672, 749, 856, 1284, 1498, 1712, 2247, 2568, 2996, 3424, 4494, 5136, 5992, 8988, 10272, 11984, 17976, 23968, 35952

Step-4: Factors of 71920

List of positive integer factors of 71920 that divides 71904 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 29, 31, 40, 58, 62, 80, 116, 124, 145, 155, 232, 248, 290, 310, 464, 496, 580, 620, 899, 1160, 1240, 1798, 2320, 2480, 3596, 4495, 7192, 8990, 14384, 17980, 35960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71904 and 71920. The biggest common factor number is the GCF number.
So the greatest common factor 71904 and 71920 is 16.

Also check out the Least Common Multiple of 71904 and 71920