Example One

Finding the greatest common factor of 91 and 315.

Start out with dividing the larger number by the smaller number to find out how many times the smaller number fits into the larger number.

315 / 91 = 3 -- 91 fits 3 times without going over

step one 315 = 91 * 3 + leftover of 42  ( 91 * 3 = 273 --- 315 - 273 = 42)

for step two the divider of step one (91) is divided by the leftover in step one (42).
91 / 42 = 2 -- 42 fits 2 times without going over

step two 91 = 42 * 2 + leftover of 7 ( 42 * 2 = 84 ----91 - 84 = 7)

for step three the divider of step two ( 42 ) is divided by the leftover of step two (7)

42/ 7 = 6 -- 7 fits fits 6 times without going over

step three 42 = 7 * 6  +  leftover of 0

When there is no leftover you have found the greatest common factor of the two numbers. The leftover in the previous step is, 7 is the greatest common factor of 91 and 315.

Divide both the numerator and denominator by 7 and your fraction will be reduced to its lowest term

91/315 = 13/45

Example Two

Find the greatest common factor of 455 and 8220

step one 8220 = 445 * 18 + 210
step two 445 = 210 * 2 + 25
step three 210 = 25 * 8 + 10
step four 25 = 10 * 2 + 5
step five 10 = 5 * 2 + 0

5 is the greatest common factor of 455 and 8220

This calculator ensures accuracy and provides the necessary breakdown of steps, helping users understand how the GCF is derived and how fractions are simplified.

The Greatest Common Factor (GCF), or the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder.
In simpler terms, the most significant number can evenly divide both (or all) of the given numbers.

Example:

For the numbers 18 and 24:

• The divisors of 18 are 1, 2, 3, 6, 9, 18
• The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

The greatest common factor between 18 and 24 is 6 because 6 is the largest number that can divide both 18 and 24 without a remainder.

Why is GCF important?

• It is used in simplifying fractions. For example, the fraction 18/24 can be simplified to 3/4 because the GCF of 18 and 24 is 6.

It's not just a theoretical concept. GCF is also helpful in solving real-world problems involving ratios, scaling, and many areas of number theory. Understanding GCF can be a powerful tool in your problem-solving arsenal.