What is the Greatest Common Factor of 75744 and 75762?

Greatest common factor (GCF) of 75744 and 75762 is 18.

GCF(75744,75762) = 18

We will now calculate the prime factors of 75744 and 75762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75744 and 75762.

How to find the GCF of 75744 and 75762?

We will first find the prime factorization of 75744 and 75762. After we will calculate the factors of 75744 and 75762 and find the biggest common factor number .

Step-1: Prime Factorization of 75744

Prime factors of 75744 are 2, 3, 263. Prime factorization of 75744 in exponential form is:

75744 = 2⁵ × 3² × 263¹

Step-2: Prime Factorization of 75762

Prime factors of 75762 are 2, 3, 23, 61. Prime factorization of 75762 in exponential form is:

75762 = 2¹ × 3³ × 23¹ × 61¹

Step-3: Factors of 75744

List of positive integer factors of 75744 that divides 75744 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 263, 288, 526, 789, 1052, 1578, 2104, 2367, 3156, 4208, 4734, 6312, 8416, 9468, 12624, 18936, 25248, 37872

Step-4: Factors of 75762

List of positive integer factors of 75762 that divides 75744 without a remainder.

1, 2, 3, 6, 9, 18, 23, 27, 46, 54, 61, 69, 122, 138, 183, 207, 366, 414, 549, 621, 1098, 1242, 1403, 1647, 2806, 3294, 4209, 8418, 12627, 25254, 37881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75744 and 75762. The biggest common factor number is the GCF number.
So the greatest common factor 75744 and 75762 is 18.

Also check out the Least Common Multiple of 75744 and 75762