How to Find GCF of 708/520, 1778/644?

GCF of 708/520, 1778/644

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 708/520, 1778/644 i.e 2/83720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 708/520, 1778/644.

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 708/520,1778/644?

Given fractions are 708/520,1778/644

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 708/520,1778/644, numerators are 708,1778

Denominators are 520,644

The GCF of 708,1778 is 2 .

LCM of 520,644 is 83720.

The greatest common factor of 708/520,1778/644 = [GCF of 708,1778]/[LCM of 520,644]= 2/83720

Therefore, the GCF of 708/520,1778/644 is 2/83720.

Greatest Common Factor of 708,1778

To find the highest common factor of 708,1778, we have to find the factors of both numbers and list the highest common factor.

The factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708

The factors of 1778 are 1, 2, 7, 14, 127, 254, 889, 1778

The HCF of 708,1778 is 2.

Lets's calculate GCF of 708,1778

Greatest Common Factor (GCF) of 708,1778 By Common Division

2	708, 1778
	354, 889

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 708,1778 By Matching Biggest Common Factor Method

Now, list down the factors of 708

1,2,3,4,6,12,59,118,177,236,354,708

Now, list down the factors of 1778

1,2,7,14,127,254,889,1778

Greatest Common Factor

We found the factors 708,1778 . The biggest common factor number is the GCF number.
So the greatest common factor 708,1778 is 2.

Lets's calculate LCM of 520,644

Lowest Common Multiple of 520,644 using Common Division

2	520, 644
2	260, 322
	130, 161

∴ So the LCM of the given numbers is 2 x 2 x 130 x 161 = 83720

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/83720

Therefore, the GCF of Fractions 708/520,1778/644 is 2/83720

Least Common Multiple of 520,644 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 520,644 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(520,644) = 4

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

GCF(520,644) x common factors =4 x 1 = 4

LCM(520,644) = ( 520 × 644 ) / 4

LCM(520,644) = 334880 / 4

LCM(520,644) = 83720

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FAQs on GCF of Fractions of 708/520, 1778/644

1. What is the HCF of 708,1778?

The HCF of 708,1778 is 2

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 708/520, 1778/644?

Answer: GCF of Numerators as per given numbers 708/520, 1778/644 is

GCF of Numerators i.e. for 708,1778 is 2

LCM of denominators i.e. for 520,644 is 83720.

Thus, GCF of Fractions is 2/83720.Finally, GCF of Fractions for 708/520, 1778/644 is 2/83720.