What is the Greatest Common Factor of 45123 and 45135?

Greatest common factor (GCF) of 45123 and 45135 is 3.

GCF(45123,45135) = 3

We will now calculate the prime factors of 45123 and 45135, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45123 and 45135.

How to find the GCF of 45123 and 45135?

We will first find the prime factorization of 45123 and 45135. After we will calculate the factors of 45123 and 45135 and find the biggest common factor number .

Step-1: Prime Factorization of 45123

Prime factors of 45123 are 3, 13, 89. Prime factorization of 45123 in exponential form is:

45123 = 3¹ × 13² × 89¹

Step-2: Prime Factorization of 45135

Prime factors of 45135 are 3, 5, 17, 59. Prime factorization of 45135 in exponential form is:

45135 = 3² × 5¹ × 17¹ × 59¹

Step-3: Factors of 45123

List of positive integer factors of 45123 that divides 45123 without a remainder.

1, 3, 13, 39, 89, 169, 267, 507, 1157, 3471, 15041

Step-4: Factors of 45135

List of positive integer factors of 45135 that divides 45123 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 59, 85, 153, 177, 255, 295, 531, 765, 885, 1003, 2655, 3009, 5015, 9027, 15045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45123 and 45135. The biggest common factor number is the GCF number.
So the greatest common factor 45123 and 45135 is 3.

Also check out the Least Common Multiple of 45123 and 45135