What is the Greatest Common Factor of 35664 and 35680?

Greatest common factor (GCF) of 35664 and 35680 is 16.

GCF(35664,35680) = 16

We will now calculate the prime factors of 35664 and 35680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35664 and 35680.

How to find the GCF of 35664 and 35680?

We will first find the prime factorization of 35664 and 35680. After we will calculate the factors of 35664 and 35680 and find the biggest common factor number .

Step-1: Prime Factorization of 35664

Prime factors of 35664 are 2, 3, 743. Prime factorization of 35664 in exponential form is:

35664 = 2⁴ × 3¹ × 743¹

Step-2: Prime Factorization of 35680

Prime factors of 35680 are 2, 5, 223. Prime factorization of 35680 in exponential form is:

35680 = 2⁵ × 5¹ × 223¹

Step-3: Factors of 35664

List of positive integer factors of 35664 that divides 35664 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 743, 1486, 2229, 2972, 4458, 5944, 8916, 11888, 17832

Step-4: Factors of 35680

List of positive integer factors of 35680 that divides 35664 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 223, 446, 892, 1115, 1784, 2230, 3568, 4460, 7136, 8920, 17840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35664 and 35680. The biggest common factor number is the GCF number.
So the greatest common factor 35664 and 35680 is 16.

Also check out the Least Common Multiple of 35664 and 35680