What is the Greatest Common Factor of 45114 and 45120?

Greatest common factor (GCF) of 45114 and 45120 is 6.

GCF(45114,45120) = 6

We will now calculate the prime factors of 45114 and 45120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45114 and 45120.

How to find the GCF of 45114 and 45120?

We will first find the prime factorization of 45114 and 45120. After we will calculate the factors of 45114 and 45120 and find the biggest common factor number .

Step-1: Prime Factorization of 45114

Prime factors of 45114 are 2, 3, 73, 103. Prime factorization of 45114 in exponential form is:

45114 = 2¹ × 3¹ × 73¹ × 103¹

Step-2: Prime Factorization of 45120

Prime factors of 45120 are 2, 3, 5, 47. Prime factorization of 45120 in exponential form is:

45120 = 2⁶ × 3¹ × 5¹ × 47¹

Step-3: Factors of 45114

List of positive integer factors of 45114 that divides 45114 without a remainder.

1, 2, 3, 6, 73, 103, 146, 206, 219, 309, 438, 618, 7519, 15038, 22557

Step-4: Factors of 45120

List of positive integer factors of 45120 that divides 45114 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 47, 48, 60, 64, 80, 94, 96, 120, 141, 160, 188, 192, 235, 240, 282, 320, 376, 470, 480, 564, 705, 752, 940, 960, 1128, 1410, 1504, 1880, 2256, 2820, 3008, 3760, 4512, 5640, 7520, 9024, 11280, 15040, 22560

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45114 and 45120. The biggest common factor number is the GCF number.
So the greatest common factor 45114 and 45120 is 6.

Also check out the Least Common Multiple of 45114 and 45120