What is the Greatest Common Factor of 35800 and 35814?

Greatest common factor (GCF) of 35800 and 35814 is 2.

GCF(35800,35814) = 2

We will now calculate the prime factors of 35800 and 35814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35800 and 35814.

How to find the GCF of 35800 and 35814?

We will first find the prime factorization of 35800 and 35814. After we will calculate the factors of 35800 and 35814 and find the biggest common factor number .

Step-1: Prime Factorization of 35800

Prime factors of 35800 are 2, 5, 179. Prime factorization of 35800 in exponential form is:

35800 = 2³ × 5² × 179¹

Step-2: Prime Factorization of 35814

Prime factors of 35814 are 2, 3, 47, 127. Prime factorization of 35814 in exponential form is:

35814 = 2¹ × 3¹ × 47¹ × 127¹

Step-3: Factors of 35800

List of positive integer factors of 35800 that divides 35800 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 179, 200, 358, 716, 895, 1432, 1790, 3580, 4475, 7160, 8950, 17900

Step-4: Factors of 35814

List of positive integer factors of 35814 that divides 35800 without a remainder.

1, 2, 3, 6, 47, 94, 127, 141, 254, 282, 381, 762, 5969, 11938, 17907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35800 and 35814. The biggest common factor number is the GCF number.
So the greatest common factor 35800 and 35814 is 2.

Also check out the Least Common Multiple of 35800 and 35814