What is the Greatest Common Factor of 45990 and 46008?

Greatest common factor (GCF) of 45990 and 46008 is 18.

GCF(45990,46008) = 18

We will now calculate the prime factors of 45990 and 46008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45990 and 46008.

How to find the GCF of 45990 and 46008?

We will first find the prime factorization of 45990 and 46008. After we will calculate the factors of 45990 and 46008 and find the biggest common factor number .

Step-1: Prime Factorization of 45990

Prime factors of 45990 are 2, 3, 5, 7, 73. Prime factorization of 45990 in exponential form is:

45990 = 2¹ × 3² × 5¹ × 7¹ × 73¹

Step-2: Prime Factorization of 46008

Prime factors of 46008 are 2, 3, 71. Prime factorization of 46008 in exponential form is:

46008 = 2³ × 3⁴ × 71¹

Step-3: Factors of 45990

List of positive integer factors of 45990 that divides 45990 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 73, 90, 105, 126, 146, 210, 219, 315, 365, 438, 511, 630, 657, 730, 1022, 1095, 1314, 1533, 2190, 2555, 3066, 3285, 4599, 5110, 6570, 7665, 9198, 15330, 22995

Step-4: Factors of 46008

List of positive integer factors of 46008 that divides 45990 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 71, 72, 81, 108, 142, 162, 213, 216, 284, 324, 426, 568, 639, 648, 852, 1278, 1704, 1917, 2556, 3834, 5112, 5751, 7668, 11502, 15336, 23004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45990 and 46008. The biggest common factor number is the GCF number.
So the greatest common factor 45990 and 46008 is 18.

Also check out the Least Common Multiple of 45990 and 46008