How to Find GCF of 468/827, 510/714?

GCF of 468/827, 510/714

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 468/827, 510/714 i.e 6/590478 easily. The following is the detailed procedure to determine the greatest common factor of fractions 468/827, 510/714.

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 468/827,510/714?

Given fractions are 468/827,510/714

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 468/827,510/714, numerators are 468,510

Denominators are 827,714

The GCF of 468,510 is 6 .

LCM of 827,714 is 590478.

The greatest common factor of 468/827,510/714 = [GCF of 468,510]/[LCM of 827,714]= 6/590478

Therefore, the GCF of 468/827,510/714 is 6/590478.

Greatest Common Factor of 468,510

To find the highest common factor of 468,510, we have to find the factors of both numbers and list the highest common factor.

The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468

The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510

The HCF of 468,510 is 6.

Lets's calculate GCF of 468,510

Greatest Common Factor (GCF) of 468,510 By Common Division

2	468, 510
3	234, 255
	78, 85

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 468,510 By Matching Biggest Common Factor Method

Now, list down the factors of 468

1,2,3,4,6,9,12,13,18,26,36,39,52,78,117,156,234,468

Now, list down the factors of 510

1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510

Greatest Common Factor

We found the factors 468,510 . The biggest common factor number is the GCF number.
So the greatest common factor 468,510 is 6.

Lets's calculate LCM of 827,714

Lowest Common Multiple of 827,714 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 590478

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/590478

Therefore, the GCF of Fractions 468/827,510/714 is 6/590478

Least Common Multiple of 827,714 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 827,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(827,714) = 1

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

GCF(827,714) x common factors =1 x 1 = 1

LCM(827,714) = ( 827 × 714 ) / 1

LCM(827,714) = 590478 / 1

LCM(827,714) = 590478

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FAQs on GCF of Fractions of 468/827, 510/714

1. What is the HCF of 468,510?

The HCF of 468,510 is 6

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 468/827, 510/714?

Answer: GCF of Numerators as per given numbers 468/827, 510/714 is

GCF of Numerators i.e. for 468,510 is 6

LCM of denominators i.e. for 827,714 is 590478.

Thus, GCF of Fractions is 6/590478.Finally, GCF of Fractions for 468/827, 510/714 is 6/590478.