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GCF of 222/83, 678/862

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 222/83, 678/862 i.e 6/71546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 222/83, 678/862.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 222/83,678/862?

Given fractions are 222/83,678/862

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 222/83,678/862, numerators are 222,678

Denominators are 83,862

The GCF of 222,678 is 6 .

LCM of 83,862 is 71546.

The greatest common factor of 222/83,678/862 = [GCF of 222,678]/[LCM of 83,862]= 6/71546

Therefore, the GCF of 222/83,678/862 is 6/71546.

Greatest Common Factor of 222,678

To find the highest common factor of 222,678, we have to find the factors of both numbers and list the highest common factor.

The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

The HCF of 222,678 is 6.

Lets's calculate GCF of 222,678

Greatest Common Factor (GCF) of 222,678 By Common Division

2 222, 678
3 111, 339
37, 113

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 222,678 By Matching Biggest Common Factor Method

Greatest Common Factor of 222,678 By Matching Biggest Common Factor Method

Now, list down the factors of 222

:

1,2,3,6,37,74,111,222

Now, list down the factors of 678

:

1,2,3,6,113,226,339,678

Greatest Common Factor

We found the factors 222,678 . The biggest common factor number is the GCF number.
So the greatest common factor 222,678 is 6.

Lets's calculate LCM of 83,862

Lowest Common Multiple of 83,862 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 71546

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/71546

Therefore, the GCF of Fractions 222/83,678/862 is 6/71546

Least Common Multiple of 83,862 with GCF Formula

Least Common Multiple of 83,862 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 83,862 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(83,862) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(83,862) x common factors =1 x 1 = 1

LCM(83,862) = ( 83 × 862 ) / 1

LCM(83,862) = 71546 / 1

LCM(83,862) = 71546


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FAQs on GCF of Fractions of 222/83, 678/862

1. What is the HCF of 222,678?

The HCF of 222,678 is 6

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 222/83, 678/862?

Answer: GCF of Numerators as per given numbers 222/83, 678/862 is

GCF of Numerators i.e. for 222,678 is 6

LCM of denominators i.e. for 83,862 is 71546.

Thus, GCF of Fractions is 6/71546.Finally, GCF of Fractions for 222/83, 678/862 is 6/71546.