How to Find GCF of 420/548, 880/222?

GCF of 420/548, 880/222

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 420/548, 880/222 i.e 20/60828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/548, 880/222.

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 420/548,880/222?

Given fractions are 420/548,880/222

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 420/548,880/222, numerators are 420,880

Denominators are 548,222

The GCF of 420,880 is 20 .

LCM of 548,222 is 60828.

The greatest common factor of 420/548,880/222 = [GCF of 420,880]/[LCM of 548,222]= 20/60828

Therefore, the GCF of 420/548,880/222 is 20/60828.

Greatest Common Factor of 420,880

To find the highest common factor of 420,880, 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 880 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880

The HCF of 420,880 is 20.

Lets's calculate GCF of 420,880

Greatest Common Factor (GCF) of 420,880 By Common Division

2	420, 880
2	210, 440
5	105, 220
	21, 44

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 420,880 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 880

1,2,4,5,8,10,11,16,20,22,40,44,55,80,88,110,176,220,440,880

Greatest Common Factor

We found the factors 420,880 . The biggest common factor number is the GCF number.
So the greatest common factor 420,880 is 20.

Lets's calculate LCM of 548,222

Lowest Common Multiple of 548,222 using Common Division

2	548, 222
	274, 111

∴ So the LCM of the given numbers is 2 x 274 x 111 = 60828

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/60828

Therefore, the GCF of Fractions 420/548,880/222 is 20/60828

Least Common Multiple of 548,222 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 548,222 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(548,222) = 2

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

GCF(548,222) x common factors =2 x 1 = 2

LCM(548,222) = ( 548 × 222 ) / 2

LCM(548,222) = 121656 / 2

LCM(548,222) = 60828

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FAQs on GCF of Fractions of 420/548, 880/222

1. What is the HCF of 420,880?

The HCF of 420,880 is 20

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 420/548, 880/222?

Answer: GCF of Numerators as per given numbers 420/548, 880/222 is

GCF of Numerators i.e. for 420,880 is 20

LCM of denominators i.e. for 548,222 is 60828.

Thus, GCF of Fractions is 20/60828.Finally, GCF of Fractions for 420/548, 880/222 is 20/60828.