What is the Greatest Common Factor of 46200 and 46208?

Greatest common factor (GCF) of 46200 and 46208 is 8.

GCF(46200,46208) = 8

We will now calculate the prime factors of 46200 and 46208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 46200 and 46208.

How to find the GCF of 46200 and 46208?

We will first find the prime factorization of 46200 and 46208. After we will calculate the factors of 46200 and 46208 and find the biggest common factor number .

Step-1: Prime Factorization of 46200

Prime factors of 46200 are 2, 3, 5, 7, 11. Prime factorization of 46200 in exponential form is:

46200 = 2³ × 3¹ × 5² × 7¹ × 11¹

Step-2: Prime Factorization of 46208

Prime factors of 46208 are 2, 19. Prime factorization of 46208 in exponential form is:

46208 = 2⁷ × 19²

Step-3: Factors of 46200

List of positive integer factors of 46200 that divides 46200 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 20, 21, 22, 24, 25, 28, 30, 33, 35, 40, 42, 44, 50, 55, 56, 60, 66, 70, 75, 77, 84, 88, 100, 105, 110, 120, 132, 140, 150, 154, 165, 168, 175, 200, 210, 220, 231, 264, 275, 280, 300, 308, 330, 350, 385, 420, 440, 462, 525, 550, 600, 616, 660, 700, 770, 825, 840, 924, 1050, 1100, 1155, 1320, 1400, 1540, 1650, 1848, 1925, 2100, 2200, 2310, 3080, 3300, 3850, 4200, 4620, 5775, 6600, 7700, 9240, 11550, 15400, 23100

Step-4: Factors of 46208

List of positive integer factors of 46208 that divides 46200 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 304, 361, 608, 722, 1216, 1444, 2432, 2888, 5776, 11552, 23104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 46200 and 46208. The biggest common factor number is the GCF number.
So the greatest common factor 46200 and 46208 is 8.

Also check out the Least Common Multiple of 46200 and 46208