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GCF of 138/632, 222/176

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 138/632, 222/176 i.e 6/13904 easily. The following is the detailed procedure to determine the greatest common factor of fractions 138/632, 222/176.

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 138/632,222/176?

Given fractions are 138/632,222/176

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 138/632,222/176, numerators are 138,222

Denominators are 632,176

The GCF of 138,222 is 6 .

LCM of 632,176 is 13904.

The greatest common factor of 138/632,222/176 = [GCF of 138,222]/[LCM of 632,176]= 6/13904

Therefore, the GCF of 138/632,222/176 is 6/13904.

Greatest Common Factor of 138,222

To find the highest common factor of 138,222, we have to find the factors of both numbers and list the highest common factor.

The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138

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

The HCF of 138,222 is 6.

Lets's calculate GCF of 138,222

Greatest Common Factor (GCF) of 138,222 By Common Division

2 138, 222
3 69, 111
23, 37

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

Greatest Common Factor of 138,222 By Matching Biggest Common Factor Method

Greatest Common Factor of 138,222 By Matching Biggest Common Factor Method

Now, list down the factors of 138

:

1,2,3,6,23,46,69,138

Now, list down the factors of 222

:

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

Greatest Common Factor

We found the factors 138,222 . The biggest common factor number is the GCF number.
So the greatest common factor 138,222 is 6.

Lets's calculate LCM of 632,176

Lowest Common Multiple of 632,176 using Common Division

2 632, 176
2 316, 88
2 158, 44
79, 22

∴ So the LCM of the given numbers is 2 x 2 x 2 x 79 x 22 = 13904

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/13904

Therefore, the GCF of Fractions 138/632,222/176 is 6/13904

Least Common Multiple of 632,176 with GCF Formula

Least Common Multiple of 632,176 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 632,176 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(632,176) = 8

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

GCF(632,176) x common factors =8 x 1 = 8

LCM(632,176) = ( 632 × 176 ) / 8

LCM(632,176) = 111232 / 8

LCM(632,176) = 13904


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FAQs on GCF of Fractions of 138/632, 222/176

1. What is the HCF of 138,222?

The HCF of 138,222 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 138/632, 222/176?

Answer: GCF of Numerators as per given numbers 138/632, 222/176 is

GCF of Numerators i.e. for 138,222 is 6

LCM of denominators i.e. for 632,176 is 13904.

Thus, GCF of Fractions is 6/13904.Finally, GCF of Fractions for 138/632, 222/176 is 6/13904.