How to Find GCF of 762/66, 280/6523?

GCF of 762/66, 280/6523

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 762/66, 280/6523 i.e 2/39138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 762/66, 280/6523.

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 762/66,280/6523?

Given fractions are 762/66,280/6523

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 762/66,280/6523, numerators are 762,280

Denominators are 66,6523

The GCF of 762,280 is 2 .

LCM of 66,6523 is 39138.

The greatest common factor of 762/66,280/6523 = [GCF of 762,280]/[LCM of 66,6523]= 2/39138

Therefore, the GCF of 762/66,280/6523 is 2/39138.

Greatest Common Factor of 762,280

To find the highest common factor of 762,280, we have to find the factors of both numbers and list the highest common factor.

The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762

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

The HCF of 762,280 is 2.

Lets's calculate GCF of 762,280

Greatest Common Factor (GCF) of 762,280 By Common Division

2	762, 280
	381, 140

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

Greatest Common Factor of 762,280 By Matching Biggest Common Factor Method

Now, list down the factors of 762

1,2,3,6,127,254,381,762

Now, list down the factors of 280

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

Greatest Common Factor

We found the factors 762,280 . The biggest common factor number is the GCF number.
So the greatest common factor 762,280 is 2.

Lets's calculate LCM of 66,6523

Lowest Common Multiple of 66,6523 using Common Division

11	66, 6523
	6, 593

∴ So the LCM of the given numbers is 11 x 6 x 593 = 39138

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/39138

Therefore, the GCF of Fractions 762/66,280/6523 is 2/39138

Least Common Multiple of 66,6523 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 66,6523 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(66,6523) = 11

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

GCF(66,6523) x common factors =11 x 1 = 11

LCM(66,6523) = ( 66 × 6523 ) / 11

LCM(66,6523) = 430518 / 11

LCM(66,6523) = 39138

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FAQs on GCF of Fractions of 762/66, 280/6523

1. What is the HCF of 762,280?

The HCF of 762,280 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 762/66, 280/6523?

Answer: GCF of Numerators as per given numbers 762/66, 280/6523 is

GCF of Numerators i.e. for 762,280 is 2

LCM of denominators i.e. for 66,6523 is 39138.

Thus, GCF of Fractions is 2/39138.Finally, GCF of Fractions for 762/66, 280/6523 is 2/39138.