How to Find GCF of 616/461, 406/275?

GCF of 616/461, 406/275

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 616/461, 406/275 i.e 14/126775 easily. The following is the detailed procedure to determine the greatest common factor of fractions 616/461, 406/275.

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 616/461,406/275?

Given fractions are 616/461,406/275

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 616/461,406/275, numerators are 616,406

Denominators are 461,275

The GCF of 616,406 is 14 .

LCM of 461,275 is 126775.

The greatest common factor of 616/461,406/275 = [GCF of 616,406]/[LCM of 461,275]= 14/126775

Therefore, the GCF of 616/461,406/275 is 14/126775.

Greatest Common Factor of 616,406

To find the highest common factor of 616,406, 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 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 616,406 is 14.

Lets's calculate GCF of 616,406

Greatest Common Factor (GCF) of 616,406 By Common Division

2	616, 406
7	308, 203
	44, 29

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 616,406 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 406

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 616,406 . The biggest common factor number is the GCF number.
So the greatest common factor 616,406 is 14.

Lets's calculate LCM of 461,275

Lowest Common Multiple of 461,275 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 126775

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/126775

Therefore, the GCF of Fractions 616/461,406/275 is 14/126775

Least Common Multiple of 461,275 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 461,275 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(461,275) = 1

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

GCF(461,275) x common factors =1 x 1 = 1

LCM(461,275) = ( 461 × 275 ) / 1

LCM(461,275) = 126775 / 1

LCM(461,275) = 126775

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FAQs on GCF of Fractions of 616/461, 406/275

1. What is the HCF of 616,406?

The HCF of 616,406 is 14

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 616/461, 406/275?

Answer: GCF of Numerators as per given numbers 616/461, 406/275 is

GCF of Numerators i.e. for 616,406 is 14

LCM of denominators i.e. for 461,275 is 126775.

Thus, GCF of Fractions is 14/126775.Finally, GCF of Fractions for 616/461, 406/275 is 14/126775.