What is the Greatest Common Factor of 19734 and 19740?

Greatest common factor (GCF) of 19734 and 19740 is 6.

GCF(19734,19740) = 6

We will now calculate the prime factors of 19734 and 19740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19734 and 19740.

How to find the GCF of 19734 and 19740?

We will first find the prime factorization of 19734 and 19740. After we will calculate the factors of 19734 and 19740 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19740

Prime factors of 19740 are 2, 3, 5, 7, 47. Prime factorization of 19740 in exponential form is:

19740 = 2² × 3¹ × 5¹ × 7¹ × 47¹

Step-3: Factors of 19734

List of positive integer factors of 19734 that divides 19734 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

Step-4: Factors of 19740

List of positive integer factors of 19740 that divides 19734 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 47, 60, 70, 84, 94, 105, 140, 141, 188, 210, 235, 282, 329, 420, 470, 564, 658, 705, 940, 987, 1316, 1410, 1645, 1974, 2820, 3290, 3948, 4935, 6580, 9870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19734 and 19740. The biggest common factor number is the GCF number.
So the greatest common factor 19734 and 19740 is 6.

Also check out the Least Common Multiple of 19734 and 19740