How to Find GCF of 420/480, 4652/566?

GCF of 420/480, 4652/566

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 420/480, 4652/566 i.e 4/135840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/480, 4652/566.

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 420/480,4652/566?

Given fractions are 420/480,4652/566

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 420/480,4652/566, numerators are 420,4652

Denominators are 480,566

The GCF of 420,4652 is 4 .

LCM of 480,566 is 135840.

The greatest common factor of 420/480,4652/566 = [GCF of 420,4652]/[LCM of 480,566]= 4/135840

Therefore, the GCF of 420/480,4652/566 is 4/135840.

Greatest Common Factor of 420,4652

To find the highest common factor of 420,4652, we have to find the factors of both numbers and list the highest common factor.

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The factors of 4652 are 1, 2, 4, 1163, 2326, 4652

The HCF of 420,4652 is 4.

Lets's calculate GCF of 420,4652

Greatest Common Factor (GCF) of 420,4652 By Common Division

2	420, 4652
2	210, 2326
	105, 1163

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 420,4652 By Matching Biggest Common Factor Method

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Now, list down the factors of 4652

1,2,4,1163,2326,4652

Greatest Common Factor

We found the factors 420,4652 . The biggest common factor number is the GCF number.
So the greatest common factor 420,4652 is 4.

Lets's calculate LCM of 480,566

Lowest Common Multiple of 480,566 using Common Division

2	480, 566
	240, 283

∴ So the LCM of the given numbers is 2 x 240 x 283 = 135840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/135840

Therefore, the GCF of Fractions 420/480,4652/566 is 4/135840

Least Common Multiple of 480,566 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 480,566 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(480,566) = 2

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

GCF(480,566) x common factors =2 x 1 = 2

LCM(480,566) = ( 480 × 566 ) / 2

LCM(480,566) = 271680 / 2

LCM(480,566) = 135840

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FAQs on GCF of Fractions of 420/480, 4652/566

1. What is the HCF of 420,4652?

The HCF of 420,4652 is 4

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 420/480, 4652/566?

Answer: GCF of Numerators as per given numbers 420/480, 4652/566 is

GCF of Numerators i.e. for 420,4652 is 4

LCM of denominators i.e. for 480,566 is 135840.

Thus, GCF of Fractions is 4/135840.Finally, GCF of Fractions for 420/480, 4652/566 is 4/135840.