What is the Greatest Common Factor of 57744 and 57750?

Greatest common factor (GCF) of 57744 and 57750 is 6.

GCF(57744,57750) = 6

We will now calculate the prime factors of 57744 and 57750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57744 and 57750.

How to find the GCF of 57744 and 57750?

We will first find the prime factorization of 57744 and 57750. After we will calculate the factors of 57744 and 57750 and find the biggest common factor number .

Step-1: Prime Factorization of 57744

Prime factors of 57744 are 2, 3, 401. Prime factorization of 57744 in exponential form is:

57744 = 2⁴ × 3² × 401¹

Step-2: Prime Factorization of 57750

Prime factors of 57750 are 2, 3, 5, 7, 11. Prime factorization of 57750 in exponential form is:

57750 = 2¹ × 3¹ × 5³ × 7¹ × 11¹

Step-3: Factors of 57744

List of positive integer factors of 57744 that divides 57744 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 401, 802, 1203, 1604, 2406, 3208, 3609, 4812, 6416, 7218, 9624, 14436, 19248, 28872

Step-4: Factors of 57750

List of positive integer factors of 57750 that divides 57744 without a remainder.

1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 25, 30, 33, 35, 42, 50, 55, 66, 70, 75, 77, 105, 110, 125, 150, 154, 165, 175, 210, 231, 250, 275, 330, 350, 375, 385, 462, 525, 550, 750, 770, 825, 875, 1050, 1155, 1375, 1650, 1750, 1925, 2310, 2625, 2750, 3850, 4125, 5250, 5775, 8250, 9625, 11550, 19250, 28875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57744 and 57750. The biggest common factor number is the GCF number.
So the greatest common factor 57744 and 57750 is 6.

Also check out the Least Common Multiple of 57744 and 57750