How to Find GCF of 520/496, 760/984?

GCF of 520/496, 760/984

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 520/496, 760/984 i.e 40/61008 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/496, 760/984.

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 520/496,760/984?

Given fractions are 520/496,760/984

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 520/496,760/984, numerators are 520,760

Denominators are 496,984

The GCF of 520,760 is 40 .

LCM of 496,984 is 61008.

The greatest common factor of 520/496,760/984 = [GCF of 520,760]/[LCM of 496,984]= 40/61008

Therefore, the GCF of 520/496,760/984 is 40/61008.

Greatest Common Factor of 520,760

To find the highest common factor of 520,760, we have to find the factors of both numbers and list the highest common factor.

The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520

The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760

The HCF of 520,760 is 40.

Lets's calculate GCF of 520,760

Greatest Common Factor (GCF) of 520,760 By Common Division

2	520, 760
2	260, 380
2	130, 190
5	65, 95
	13, 19

∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40

Greatest Common Factor of 520,760 By Matching Biggest Common Factor Method

Now, list down the factors of 520

1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520

Now, list down the factors of 760

1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760

Greatest Common Factor

We found the factors 520,760 . The biggest common factor number is the GCF number.
So the greatest common factor 520,760 is 40.

Lets's calculate LCM of 496,984

Lowest Common Multiple of 496,984 using Common Division

2	496, 984
2	248, 492
2	124, 246
	62, 123

∴ So the LCM of the given numbers is 2 x 2 x 2 x 62 x 123 = 61008

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/61008

Therefore, the GCF of Fractions 520/496,760/984 is 40/61008

Least Common Multiple of 496,984 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 496,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(496,984) = 8

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

GCF(496,984) x common factors =8 x 1 = 8

LCM(496,984) = ( 496 × 984 ) / 8

LCM(496,984) = 488064 / 8

LCM(496,984) = 61008

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FAQs on GCF of Fractions of 520/496, 760/984

1. What is the HCF of 520,760?

The HCF of 520,760 is 40

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 520/496, 760/984?

Answer: GCF of Numerators as per given numbers 520/496, 760/984 is

GCF of Numerators i.e. for 520,760 is 40

LCM of denominators i.e. for 496,984 is 61008.

Thus, GCF of Fractions is 40/61008.Finally, GCF of Fractions for 520/496, 760/984 is 40/61008.