What is the Greatest Common Factor of 46980 and 47000?

Greatest common factor (GCF) of 46980 and 47000 is 20.

GCF(46980,47000) = 20

We will now calculate the prime factors of 46980 and 47000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 46980 and 47000.

How to find the GCF of 46980 and 47000?

We will first find the prime factorization of 46980 and 47000. After we will calculate the factors of 46980 and 47000 and find the biggest common factor number .

Step-1: Prime Factorization of 46980

Prime factors of 46980 are 2, 3, 5, 29. Prime factorization of 46980 in exponential form is:

46980 = 2² × 3⁴ × 5¹ × 29¹

Step-2: Prime Factorization of 47000

Prime factors of 47000 are 2, 5, 47. Prime factorization of 47000 in exponential form is:

47000 = 2³ × 5³ × 47¹

Step-3: Factors of 46980

List of positive integer factors of 46980 that divides 46980 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 29, 30, 36, 45, 54, 58, 60, 81, 87, 90, 108, 116, 135, 145, 162, 174, 180, 261, 270, 290, 324, 348, 405, 435, 522, 540, 580, 783, 810, 870, 1044, 1305, 1566, 1620, 1740, 2349, 2610, 3132, 3915, 4698, 5220, 7830, 9396, 11745, 15660, 23490

Step-4: Factors of 47000

List of positive integer factors of 47000 that divides 46980 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 47, 50, 94, 100, 125, 188, 200, 235, 250, 376, 470, 500, 940, 1000, 1175, 1880, 2350, 4700, 5875, 9400, 11750, 23500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 46980 and 47000. The biggest common factor number is the GCF number.
So the greatest common factor 46980 and 47000 is 20.

Also check out the Least Common Multiple of 46980 and 47000