How to Find GCF of 560/314, 616/757?

GCF of 560/314, 616/757

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 560/314, 616/757 i.e 56/237698 easily. The following is the detailed procedure to determine the greatest common factor of fractions 560/314, 616/757.

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 560/314,616/757?

Given fractions are 560/314,616/757

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 560/314,616/757, numerators are 560,616

Denominators are 314,757

The GCF of 560,616 is 56 .

LCM of 314,757 is 237698.

The greatest common factor of 560/314,616/757 = [GCF of 560,616]/[LCM of 314,757]= 56/237698

Therefore, the GCF of 560/314,616/757 is 56/237698.

Greatest Common Factor of 560,616

To find the highest common factor of 560,616, we have to find the factors of both numbers and list the highest common factor.

The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560

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

The HCF of 560,616 is 56.

Lets's calculate GCF of 560,616

Greatest Common Factor (GCF) of 560,616 By Common Division

2	560, 616
2	280, 308
2	140, 154
7	70, 77
	10, 11

∴ So the GCF of the given numbers is 2 x 2 x 2 x 7 = 56

Greatest Common Factor of 560,616 By Matching Biggest Common Factor Method

Now, list down the factors of 560

1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560

Now, list down the factors of 616

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

Greatest Common Factor

We found the factors 560,616 . The biggest common factor number is the GCF number.
So the greatest common factor 560,616 is 56.

Lets's calculate LCM of 314,757

Lowest Common Multiple of 314,757 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 237698

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 56/237698

Therefore, the GCF of Fractions 560/314,616/757 is 56/237698

Least Common Multiple of 314,757 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 314,757 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,757) = 1

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

GCF(314,757) x common factors =1 x 1 = 1

LCM(314,757) = ( 314 × 757 ) / 1

LCM(314,757) = 237698 / 1

LCM(314,757) = 237698

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FAQs on GCF of Fractions of 560/314, 616/757

1. What is the HCF of 560,616?

The HCF of 560,616 is 56

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 560/314, 616/757?

Answer: GCF of Numerators as per given numbers 560/314, 616/757 is

GCF of Numerators i.e. for 560,616 is 56

LCM of denominators i.e. for 314,757 is 237698.

Thus, GCF of Fractions is 56/237698.Finally, GCF of Fractions for 560/314, 616/757 is 56/237698.