What is the Greatest Common Factor of 69904 and 69920?

Greatest common factor (GCF) of 69904 and 69920 is 16.

GCF(69904,69920) = 16

We will now calculate the prime factors of 69904 and 69920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69904 and 69920.

How to find the GCF of 69904 and 69920?

We will first find the prime factorization of 69904 and 69920. After we will calculate the factors of 69904 and 69920 and find the biggest common factor number .

Step-1: Prime Factorization of 69904

Prime factors of 69904 are 2, 17, 257. Prime factorization of 69904 in exponential form is:

69904 = 2⁴ × 17¹ × 257¹

Step-2: Prime Factorization of 69920

Prime factors of 69920 are 2, 5, 19, 23. Prime factorization of 69920 in exponential form is:

69920 = 2⁵ × 5¹ × 19¹ × 23¹

Step-3: Factors of 69904

List of positive integer factors of 69904 that divides 69904 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 257, 272, 514, 1028, 2056, 4112, 4369, 8738, 17476, 34952

Step-4: Factors of 69920

List of positive integer factors of 69920 that divides 69904 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 23, 32, 38, 40, 46, 76, 80, 92, 95, 115, 152, 160, 184, 190, 230, 304, 368, 380, 437, 460, 608, 736, 760, 874, 920, 1520, 1748, 1840, 2185, 3040, 3496, 3680, 4370, 6992, 8740, 13984, 17480, 34960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69904 and 69920. The biggest common factor number is the GCF number.
So the greatest common factor 69904 and 69920 is 16.

Also check out the Least Common Multiple of 69904 and 69920