What is the Greatest Common Factor of 19725 and 19734?

Greatest common factor (GCF) of 19725 and 19734 is 3.

GCF(19725,19734) = 3

We will now calculate the prime factors of 19725 and 19734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19725 and 19734.

How to find the GCF of 19725 and 19734?

We will first find the prime factorization of 19725 and 19734. After we will calculate the factors of 19725 and 19734 and find the biggest common factor number .

Step-1: Prime Factorization of 19725

Prime factors of 19725 are 3, 5, 263. Prime factorization of 19725 in exponential form is:

19725 = 3¹ × 5² × 263¹

Step-2: Prime Factorization of 19734

Prime factors of 19734 are 2, 3, 11, 13, 23. Prime factorization of 19734 in exponential form is:

19734 = 2¹ × 3¹ × 11¹ × 13¹ × 23¹

Step-3: Factors of 19725

List of positive integer factors of 19725 that divides 19725 without a remainder.

1, 3, 5, 15, 25, 75, 263, 789, 1315, 3945, 6575

Step-4: Factors of 19734

List of positive integer factors of 19734 that divides 19725 without a remainder.

1, 2, 3, 6, 11, 13, 22, 23, 26, 33, 39, 46, 66, 69, 78, 138, 143, 253, 286, 299, 429, 506, 598, 759, 858, 897, 1518, 1794, 3289, 6578, 9867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19725 and 19734. The biggest common factor number is the GCF number.
So the greatest common factor 19725 and 19734 is 3.

Also check out the Least Common Multiple of 19725 and 19734