What is the Greatest Common Factor of 22496 and 22512?

Greatest common factor (GCF) of 22496 and 22512 is 16.

GCF(22496,22512) = 16

We will now calculate the prime factors of 22496 and 22512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22496 and 22512.

How to find the GCF of 22496 and 22512?

We will first find the prime factorization of 22496 and 22512. After we will calculate the factors of 22496 and 22512 and find the biggest common factor number .

Step-1: Prime Factorization of 22496

Prime factors of 22496 are 2, 19, 37. Prime factorization of 22496 in exponential form is:

22496 = 2⁵ × 19¹ × 37¹

Step-2: Prime Factorization of 22512

Prime factors of 22512 are 2, 3, 7, 67. Prime factorization of 22512 in exponential form is:

22512 = 2⁴ × 3¹ × 7¹ × 67¹

Step-3: Factors of 22496

List of positive integer factors of 22496 that divides 22496 without a remainder.

1, 2, 4, 8, 16, 19, 32, 37, 38, 74, 76, 148, 152, 296, 304, 592, 608, 703, 1184, 1406, 2812, 5624, 11248

Step-4: Factors of 22512

List of positive integer factors of 22512 that divides 22496 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 67, 84, 112, 134, 168, 201, 268, 336, 402, 469, 536, 804, 938, 1072, 1407, 1608, 1876, 2814, 3216, 3752, 5628, 7504, 11256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22496 and 22512. The biggest common factor number is the GCF number.
So the greatest common factor 22496 and 22512 is 16.

Also check out the Least Common Multiple of 22496 and 22512