What is the Greatest Common Factor of 45990 and 46004?

Greatest common factor (GCF) of 45990 and 46004 is 14.

GCF(45990,46004) = 14

We will now calculate the prime factors of 45990 and 46004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45990 and 46004.

How to find the GCF of 45990 and 46004?

We will first find the prime factorization of 45990 and 46004. After we will calculate the factors of 45990 and 46004 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 46004

Prime factors of 46004 are 2, 7, 31, 53. Prime factorization of 46004 in exponential form is:

46004 = 2² × 7¹ × 31¹ × 53¹

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 46004

List of positive integer factors of 46004 that divides 45990 without a remainder.

1, 2, 4, 7, 14, 28, 31, 53, 62, 106, 124, 212, 217, 371, 434, 742, 868, 1484, 1643, 3286, 6572, 11501, 23002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45990 and 46004. The biggest common factor number is the GCF number.
So the greatest common factor 45990 and 46004 is 14.

Also check out the Least Common Multiple of 45990 and 46004