What is the Greatest Common Factor of 67632 and 67648?

Greatest common factor (GCF) of 67632 and 67648 is 16.

GCF(67632,67648) = 16

We will now calculate the prime factors of 67632 and 67648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67632 and 67648.

How to find the GCF of 67632 and 67648?

We will first find the prime factorization of 67632 and 67648. After we will calculate the factors of 67632 and 67648 and find the biggest common factor number .

Step-1: Prime Factorization of 67632

Prime factors of 67632 are 2, 3, 1409. Prime factorization of 67632 in exponential form is:

67632 = 2⁴ × 3¹ × 1409¹

Step-2: Prime Factorization of 67648

Prime factors of 67648 are 2, 7, 151. Prime factorization of 67648 in exponential form is:

67648 = 2⁶ × 7¹ × 151¹

Step-3: Factors of 67632

List of positive integer factors of 67632 that divides 67632 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1409, 2818, 4227, 5636, 8454, 11272, 16908, 22544, 33816

Step-4: Factors of 67648

List of positive integer factors of 67648 that divides 67632 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 151, 224, 302, 448, 604, 1057, 1208, 2114, 2416, 4228, 4832, 8456, 9664, 16912, 33824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67632 and 67648. The biggest common factor number is the GCF number.
So the greatest common factor 67632 and 67648 is 16.

Also check out the Least Common Multiple of 67632 and 67648