What is the Greatest Common Factor of 19740 and 19750?

Greatest common factor (GCF) of 19740 and 19750 is 10.

GCF(19740,19750) = 10

We will now calculate the prime factors of 19740 and 19750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19740 and 19750.

How to find the GCF of 19740 and 19750?

We will first find the prime factorization of 19740 and 19750. After we will calculate the factors of 19740 and 19750 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19750

Prime factors of 19750 are 2, 5, 79. Prime factorization of 19750 in exponential form is:

19750 = 2¹ × 5³ × 79¹

Step-3: Factors of 19740

List of positive integer factors of 19740 that divides 19740 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

Step-4: Factors of 19750

List of positive integer factors of 19750 that divides 19740 without a remainder.

1, 2, 5, 10, 25, 50, 79, 125, 158, 250, 395, 790, 1975, 3950, 9875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19740 and 19750. The biggest common factor number is the GCF number.
So the greatest common factor 19740 and 19750 is 10.

Also check out the Least Common Multiple of 19740 and 19750