What is the Greatest Common Factor of 37734 and 37753?

Greatest common factor (GCF) of 37734 and 37753 is 19.

GCF(37734,37753) = 19

We will now calculate the prime factors of 37734 and 37753, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37734 and 37753.

How to find the GCF of 37734 and 37753?

We will first find the prime factorization of 37734 and 37753. After we will calculate the factors of 37734 and 37753 and find the biggest common factor number .

Step-1: Prime Factorization of 37734

Prime factors of 37734 are 2, 3, 19, 331. Prime factorization of 37734 in exponential form is:

37734 = 2¹ × 3¹ × 19¹ × 331¹

Step-2: Prime Factorization of 37753

Prime factors of 37753 are 19, 1987. Prime factorization of 37753 in exponential form is:

37753 = 19¹ × 1987¹

Step-3: Factors of 37734

List of positive integer factors of 37734 that divides 37734 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 331, 662, 993, 1986, 6289, 12578, 18867

Step-4: Factors of 37753

List of positive integer factors of 37753 that divides 37734 without a remainder.

1, 19, 1987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37734 and 37753. The biggest common factor number is the GCF number.
So the greatest common factor 37734 and 37753 is 19.

Also check out the Least Common Multiple of 37734 and 37753