How to Find GCF of 46/480, 8278/3970?

GCF of 46/480, 8278/3970

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 46/480, 8278/3970 i.e 2/190560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/480, 8278/3970.

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 46/480,8278/3970?

Given fractions are 46/480,8278/3970

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 46/480,8278/3970, numerators are 46,8278

Denominators are 480,3970

The GCF of 46,8278 is 2 .

LCM of 480,3970 is 190560.

The greatest common factor of 46/480,8278/3970 = [GCF of 46,8278]/[LCM of 480,3970]= 2/190560

Therefore, the GCF of 46/480,8278/3970 is 2/190560.

Greatest Common Factor of 46,8278

To find the highest common factor of 46,8278, we have to find the factors of both numbers and list the highest common factor.

The factors of 46 are 1, 2, 23, 46

The factors of 8278 are 1, 2, 4139, 8278

The HCF of 46,8278 is 2.

Lets's calculate GCF of 46,8278

Greatest Common Factor (GCF) of 46,8278 By Common Division

2	46, 8278
	23, 4139

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

Greatest Common Factor of 46,8278 By Matching Biggest Common Factor Method

Now, list down the factors of 46

1,2,23,46

Now, list down the factors of 8278

1,2,4139,8278

Greatest Common Factor

We found the factors 46,8278 . The biggest common factor number is the GCF number.
So the greatest common factor 46,8278 is 2.

Lets's calculate LCM of 480,3970

Lowest Common Multiple of 480,3970 using Common Division

2	480, 3970
5	240, 1985
	48, 397

∴ So the LCM of the given numbers is 2 x 5 x 48 x 397 = 190560

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/190560

Therefore, the GCF of Fractions 46/480,8278/3970 is 2/190560

Least Common Multiple of 480,3970 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 480,3970 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(480,3970) = 10

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

GCF(480,3970) x common factors =10 x 1 = 10

LCM(480,3970) = ( 480 × 3970 ) / 10

LCM(480,3970) = 1905600 / 10

LCM(480,3970) = 190560

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FAQs on GCF of Fractions of 46/480, 8278/3970

1. What is the HCF of 46,8278?

The HCF of 46,8278 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 46/480, 8278/3970?

Answer: GCF of Numerators as per given numbers 46/480, 8278/3970 is

GCF of Numerators i.e. for 46,8278 is 2

LCM of denominators i.e. for 480,3970 is 190560.

Thus, GCF of Fractions is 2/190560.Finally, GCF of Fractions for 46/480, 8278/3970 is 2/190560.