What is the Greatest Common Factor of 81744 and 81762?

Greatest common factor (GCF) of 81744 and 81762 is 6.

GCF(81744,81762) = 6

We will now calculate the prime factors of 81744 and 81762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81744 and 81762.

How to find the GCF of 81744 and 81762?

We will first find the prime factorization of 81744 and 81762. After we will calculate the factors of 81744 and 81762 and find the biggest common factor number .

Step-1: Prime Factorization of 81744

Prime factors of 81744 are 2, 3, 13, 131. Prime factorization of 81744 in exponential form is:

81744 = 2⁴ × 3¹ × 13¹ × 131¹

Step-2: Prime Factorization of 81762

Prime factors of 81762 are 2, 3, 13627. Prime factorization of 81762 in exponential form is:

81762 = 2¹ × 3¹ × 13627¹

Step-3: Factors of 81744

List of positive integer factors of 81744 that divides 81744 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 131, 156, 208, 262, 312, 393, 524, 624, 786, 1048, 1572, 1703, 2096, 3144, 3406, 5109, 6288, 6812, 10218, 13624, 20436, 27248, 40872

Step-4: Factors of 81762

List of positive integer factors of 81762 that divides 81744 without a remainder.

1, 2, 3, 6, 13627, 27254, 40881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81744 and 81762. The biggest common factor number is the GCF number.
So the greatest common factor 81744 and 81762 is 6.

Also check out the Least Common Multiple of 81744 and 81762