How to Find GCF of 616/183, 154/422?

GCF of 616/183, 154/422

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 616/183, 154/422 i.e 154/77226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 616/183, 154/422.

Enter two or more fractions separated by "commas"

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

What is the GCF of 616/183,154/422?

Given fractions are 616/183,154/422

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 616/183,154/422, numerators are 616,154

Denominators are 183,422

The GCF of 616,154 is 154 .

LCM of 183,422 is 77226.

The greatest common factor of 616/183,154/422 = [GCF of 616,154]/[LCM of 183,422]= 154/77226

Therefore, the GCF of 616/183,154/422 is 154/77226.

Greatest Common Factor of 616,154

To find the highest common factor of 616,154, we have to find the factors of both numbers and list the highest common factor.

The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616

The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154

The HCF of 616,154 is 154.

Lets's calculate GCF of 616,154

Greatest Common Factor (GCF) of 616,154 By Common Division

2	616, 154
7	308, 77
11	44, 11
	4, 1

∴ So the GCF of the given numbers is 2 x 7 x 11 = 154

Greatest Common Factor of 616,154 By Matching Biggest Common Factor Method

Now, list down the factors of 616

1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616

Now, list down the factors of 154

1,2,7,11,14,22,77,154

Greatest Common Factor

We found the factors 616,154 . The biggest common factor number is the GCF number.
So the greatest common factor 616,154 is 154.

Lets's calculate LCM of 183,422

Lowest Common Multiple of 183,422 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 77226

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 154/77226

Therefore, the GCF of Fractions 616/183,154/422 is 154/77226

Least Common Multiple of 183,422 with GCF Formula

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

We need to calculate greatest common factor of 183,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(183,422) = 1

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

GCF(183,422) x common factors =1 x 1 = 1

LCM(183,422) = ( 183 × 422 ) / 1

LCM(183,422) = 77226 / 1

LCM(183,422) = 77226

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FAQs on GCF of Fractions of 616/183, 154/422

1. What is the HCF of 616,154?

The HCF of 616,154 is 154

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 616/183, 154/422?

Answer: GCF of Numerators as per given numbers 616/183, 154/422 is

GCF of Numerators i.e. for 616,154 is 154

LCM of denominators i.e. for 183,422 is 77226.

Thus, GCF of Fractions is 154/77226.Finally, GCF of Fractions for 616/183, 154/422 is 154/77226.