What is the Greatest Common Factor of 35872 and 35888?

Greatest common factor (GCF) of 35872 and 35888 is 16.

GCF(35872,35888) = 16

We will now calculate the prime factors of 35872 and 35888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35872 and 35888.

How to find the GCF of 35872 and 35888?

We will first find the prime factorization of 35872 and 35888. After we will calculate the factors of 35872 and 35888 and find the biggest common factor number .

Step-1: Prime Factorization of 35872

Prime factors of 35872 are 2, 19, 59. Prime factorization of 35872 in exponential form is:

35872 = 2⁵ × 19¹ × 59¹

Step-2: Prime Factorization of 35888

Prime factors of 35888 are 2, 2243. Prime factorization of 35888 in exponential form is:

35888 = 2⁴ × 2243¹

Step-3: Factors of 35872

List of positive integer factors of 35872 that divides 35872 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 59, 76, 118, 152, 236, 304, 472, 608, 944, 1121, 1888, 2242, 4484, 8968, 17936

Step-4: Factors of 35888

List of positive integer factors of 35888 that divides 35872 without a remainder.

1, 2, 4, 8, 16, 2243, 4486, 8972, 17944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35872 and 35888. The biggest common factor number is the GCF number.
So the greatest common factor 35872 and 35888 is 16.

Also check out the Least Common Multiple of 35872 and 35888