How to Find GCF of 408/732, 510/816?

GCF of 408/732, 510/816

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 408/732, 510/816 i.e 102/49776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/732, 510/816.

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 408/732,510/816?

Given fractions are 408/732,510/816

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 408/732,510/816, numerators are 408,510

Denominators are 732,816

The GCF of 408,510 is 102 .

LCM of 732,816 is 49776.

The greatest common factor of 408/732,510/816 = [GCF of 408,510]/[LCM of 732,816]= 102/49776

Therefore, the GCF of 408/732,510/816 is 102/49776.

Greatest Common Factor of 408,510

To find the highest common factor of 408,510, we have to find the factors of both numbers and list the highest common factor.

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

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

The HCF of 408,510 is 102.

Lets's calculate GCF of 408,510

Greatest Common Factor (GCF) of 408,510 By Common Division

2	408, 510
3	204, 255
17	68, 85
	4, 5

∴ So the GCF of the given numbers is 2 x 3 x 17 = 102

Greatest Common Factor of 408,510 By Matching Biggest Common Factor Method

Now, list down the factors of 408

1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408

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 408,510 . The biggest common factor number is the GCF number.
So the greatest common factor 408,510 is 102.

Lets's calculate LCM of 732,816

Lowest Common Multiple of 732,816 using Common Division

2	732, 816
2	366, 408
3	183, 204
	61, 68

∴ So the LCM of the given numbers is 2 x 2 x 3 x 61 x 68 = 49776

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 102/49776

Therefore, the GCF of Fractions 408/732,510/816 is 102/49776

Least Common Multiple of 732,816 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 732,816 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(732,816) = 12

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

GCF(732,816) x common factors =12 x 1 = 12

LCM(732,816) = ( 732 × 816 ) / 12

LCM(732,816) = 597312 / 12

LCM(732,816) = 49776

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FAQs on GCF of Fractions of 408/732, 510/816

1. What is the HCF of 408,510?

The HCF of 408,510 is 102

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 408/732, 510/816?

Answer: GCF of Numerators as per given numbers 408/732, 510/816 is

GCF of Numerators i.e. for 408,510 is 102

LCM of denominators i.e. for 732,816 is 49776.

Thus, GCF of Fractions is 102/49776.Finally, GCF of Fractions for 408/732, 510/816 is 102/49776.