What is the Greatest Common Factor of 75509 and 75516?

Greatest common factor (GCF) of 75509 and 75516 is 7.

GCF(75509,75516) = 7

We will now calculate the prime factors of 75509 and 75516, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75509 and 75516.

How to find the GCF of 75509 and 75516?

We will first find the prime factorization of 75509 and 75516. After we will calculate the factors of 75509 and 75516 and find the biggest common factor number .

Step-1: Prime Factorization of 75509

Prime factors of 75509 are 7, 23, 67. Prime factorization of 75509 in exponential form is:

75509 = 7² × 23¹ × 67¹

Step-2: Prime Factorization of 75516

Prime factors of 75516 are 2, 3, 7, 29, 31. Prime factorization of 75516 in exponential form is:

75516 = 2² × 3¹ × 7¹ × 29¹ × 31¹

Step-3: Factors of 75509

List of positive integer factors of 75509 that divides 75509 without a remainder.

1, 7, 23, 49, 67, 161, 469, 1127, 1541, 3283, 10787

Step-4: Factors of 75516

List of positive integer factors of 75516 that divides 75509 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 29, 31, 42, 58, 62, 84, 87, 93, 116, 124, 174, 186, 203, 217, 348, 372, 406, 434, 609, 651, 812, 868, 899, 1218, 1302, 1798, 2436, 2604, 2697, 3596, 5394, 6293, 10788, 12586, 18879, 25172, 37758

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75509 and 75516. The biggest common factor number is the GCF number.
So the greatest common factor 75509 and 75516 is 7.

Also check out the Least Common Multiple of 75509 and 75516