How to Find GCF of 510/178, 420/737?

GCF of 510/178, 420/737

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 510/178, 420/737 i.e 30/131186 easily. The following is the detailed procedure to determine the greatest common factor of fractions 510/178, 420/737.

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 510/178,420/737?

Given fractions are 510/178,420/737

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 510/178,420/737, numerators are 510,420

Denominators are 178,737

The GCF of 510,420 is 30 .

LCM of 178,737 is 131186.

The greatest common factor of 510/178,420/737 = [GCF of 510,420]/[LCM of 178,737]= 30/131186

Therefore, the GCF of 510/178,420/737 is 30/131186.

Greatest Common Factor of 510,420

To find the highest common factor of 510,420, we have to find the factors of both numbers and list the highest common factor.

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

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 HCF of 510,420 is 30.

Lets's calculate GCF of 510,420

Greatest Common Factor (GCF) of 510,420 By Common Division

2	510, 420
3	255, 210
5	85, 70
	17, 14

∴ So the GCF of the given numbers is 2 x 3 x 5 = 30

Greatest Common Factor of 510,420 By Matching Biggest Common Factor Method

Now, list down the factors of 510

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

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

Greatest Common Factor

We found the factors 510,420 . The biggest common factor number is the GCF number.
So the greatest common factor 510,420 is 30.

Lets's calculate LCM of 178,737

Lowest Common Multiple of 178,737 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 131186

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/131186

Therefore, the GCF of Fractions 510/178,420/737 is 30/131186

Least Common Multiple of 178,737 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 178,737 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(178,737) = 1

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

GCF(178,737) x common factors =1 x 1 = 1

LCM(178,737) = ( 178 × 737 ) / 1

LCM(178,737) = 131186 / 1

LCM(178,737) = 131186

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FAQs on GCF of Fractions of 510/178, 420/737

1. What is the HCF of 510,420?

The HCF of 510,420 is 30

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 510/178, 420/737?

Answer: GCF of Numerators as per given numbers 510/178, 420/737 is

GCF of Numerators i.e. for 510,420 is 30

LCM of denominators i.e. for 178,737 is 131186.

Thus, GCF of Fractions is 30/131186.Finally, GCF of Fractions for 510/178, 420/737 is 30/131186.