What is the Greatest Common Factor of 31344 and 31350?

Greatest common factor (GCF) of 31344 and 31350 is 6.

GCF(31344,31350) = 6

We will now calculate the prime factors of 31344 and 31350, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31344 and 31350.

How to find the GCF of 31344 and 31350?

We will first find the prime factorization of 31344 and 31350. After we will calculate the factors of 31344 and 31350 and find the biggest common factor number .

Step-1: Prime Factorization of 31344

Prime factors of 31344 are 2, 3, 653. Prime factorization of 31344 in exponential form is:

31344 = 2⁴ × 3¹ × 653¹

Step-2: Prime Factorization of 31350

Prime factors of 31350 are 2, 3, 5, 11, 19. Prime factorization of 31350 in exponential form is:

31350 = 2¹ × 3¹ × 5² × 11¹ × 19¹

Step-3: Factors of 31344

List of positive integer factors of 31344 that divides 31344 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 653, 1306, 1959, 2612, 3918, 5224, 7836, 10448, 15672

Step-4: Factors of 31350

List of positive integer factors of 31350 that divides 31344 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 19, 22, 25, 30, 33, 38, 50, 55, 57, 66, 75, 95, 110, 114, 150, 165, 190, 209, 275, 285, 330, 418, 475, 550, 570, 627, 825, 950, 1045, 1254, 1425, 1650, 2090, 2850, 3135, 5225, 6270, 10450, 15675

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31344 and 31350. The biggest common factor number is the GCF number.
So the greatest common factor 31344 and 31350 is 6.

Also check out the Least Common Multiple of 31344 and 31350