Greatest Common Factor

The greatest common factor is the greatest factor that divides two or more than two numbers. In general, it is abbreviated as GCF. Greatest common divisor (GCD), greatest common denominator (GCD), and highest common factors (HCF) are other names of GCF. For example, let any two numbers A and B. The greatest factor that divides both A and B is C. Therefore, C is the GCF of A and B. In some cases, there is no greatest factor that divides the given numbers. For such cases, 1 is the GCF of the given numbers.

The Calculator:

This online calculator is one of the best means to carry out your problems on GCF. All you have to enter two or more whole numbers and separate them by using commas between them. Click on the ‘Calculate’ button. The calculations and the result will get displayed on the screen.

Finding GCF by Prime Factorisation Method:

• Write the prime factors of each of the given whole numbers.
• Point out the common prime factors that are present in the prime factors of the given numbers.
• At last, multiply all the common prime factors to get the required result.

Follow all these steps for the calculation to get the required result. For example, if we have to find the GCF of 20 and 30.

• The prime factors of 20 are 2, 2, and 5.
• The prime factors of 30 are 2, 3, and 5.
• The common prime factors of 20 and 30 are 2 and 5.
• Then multiplying 2 and 5: 2 * 5 = 10.
• The GCF of 20 and 30 is 10.

Finding GCF by Factoring:

• Firstly, we have to write down the factors of the given numbers.
• Make out the list of the factors that are common in all the given numbers.
• After that choose the greatest number from the list of the common factors.
• The greatest number is the GCF of the given numbers.

For example, find the GCF of 5 and 15.

• The factors of 5 are 1 and 5.
• The factors of 10 are 1, 2, and 5.
• The common factors of 5 and 10 are 1 and 5.
• The greatest number is 5.
• Therefore, GCF of 5 and 15 is 5.

Finding GCF by Euclid’s algorithm:

When we have to find the GCF of very large numbers then we use this method. For example, the GCF of 6543, 7653, and 5689 gets calculated by this method easily.

• Suppose we have two given whole numbers. Subtract the smaller number from the larger number.
• If the result is greater than the smaller number. Then you have to subtract the smaller number from the result. Repeat the process until you get the result smaller than the earliest smaller number.
• After that, make the result as the new smaller number and the earliest smaller number as the new larger number.
• You have to follow the same process as earlier until you get the final result zero.
• The smallest result in the process just before zero is the GCF of the given two numbers.

For example, find the GCF of 18 and 27.

• 27 - 18 = 9.
• 18 - 9 = 9.
• 9 – 9 = 0.
• That means 9 is the GCF of 18 and 27.

In case of three whole numbers, the GCF of two larger numbers is find out first. After doing that, take the result and the smallest number and repeat the Euclid’s algorithm. This result is the final GCF of the given three whole numbers.