What is the Greatest Common Factor of 1740 and 1752?

Greatest common factor (GCF) of 1740 and 1752 is 12.

GCF(1740,1752) = 12

We will now calculate the prime factors of 1740 and 1752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1740 and 1752.

How to find the GCF of 1740 and 1752?

We will first find the prime factorization of 1740 and 1752. After we will calculate the factors of 1740 and 1752 and find the biggest common factor number .

Step-1: Prime Factorization of 1740

Prime factors of 1740 are 2, 3, 5, 29. Prime factorization of 1740 in exponential form is:

1740 = 2² × 3¹ × 5¹ × 29¹

Step-2: Prime Factorization of 1752

Prime factors of 1752 are 2, 3, 73. Prime factorization of 1752 in exponential form is:

1752 = 2³ × 3¹ × 73¹

Step-3: Factors of 1740

List of positive integer factors of 1740 that divides 1740 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870

Step-4: Factors of 1752

List of positive integer factors of 1752 that divides 1740 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 73, 146, 219, 292, 438, 584, 876

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1740 and 1752. The biggest common factor number is the GCF number.
So the greatest common factor 1740 and 1752 is 12.

Also check out the Least Common Multiple of 1740 and 1752