What is the Greatest Common Factor of 83742 and 83760?

Greatest common factor (GCF) of 83742 and 83760 is 6.

GCF(83742,83760) = 6

We will now calculate the prime factors of 83742 and 83760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83742 and 83760.

How to find the GCF of 83742 and 83760?

We will first find the prime factorization of 83742 and 83760. After we will calculate the factors of 83742 and 83760 and find the biggest common factor number .

Step-1: Prime Factorization of 83742

Prime factors of 83742 are 2, 3, 17, 821. Prime factorization of 83742 in exponential form is:

83742 = 2¹ × 3¹ × 17¹ × 821¹

Step-2: Prime Factorization of 83760

Prime factors of 83760 are 2, 3, 5, 349. Prime factorization of 83760 in exponential form is:

83760 = 2⁴ × 3¹ × 5¹ × 349¹

Step-3: Factors of 83742

List of positive integer factors of 83742 that divides 83742 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 821, 1642, 2463, 4926, 13957, 27914, 41871

Step-4: Factors of 83760

List of positive integer factors of 83760 that divides 83742 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 349, 698, 1047, 1396, 1745, 2094, 2792, 3490, 4188, 5235, 5584, 6980, 8376, 10470, 13960, 16752, 20940, 27920, 41880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83742 and 83760. The biggest common factor number is the GCF number.
So the greatest common factor 83742 and 83760 is 6.

Also check out the Least Common Multiple of 83742 and 83760