How to Find GCF of 42/70, 12/43, 878/411?

GCF of 42/70, 12/43, 878/411

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 42/70, 12/43, 878/411 i.e 2/1237110 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/70, 12/43, 878/411.

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 42/70,12/43,878/411?

Given fractions are 42/70,12/43,878/411

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 42/70,12/43,878/411, numerators are 42,12,878

Denominators are 70,43,411

The GCF of 42,12,878 is 2 .

LCM of 70,43,411 is 1237110.

The greatest common factor of 42/70,12/43,878/411 = [GCF of 42,12,878]/[LCM of 70,43,411]= 2/1237110

Therefore, the GCF of 42/70,12/43,878/411 is 2/1237110.

Greatest Common Factor of 42,12,878

To find the highest common factor of 42,12,878, we have to find the factors of both numbers and list the highest common factor.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 12 are 1, 2, 3, 4, 6, 12

The factors of 878 are 1, 2, 439, 878

The HCF of 42,12,878 is 2.

Lets's calculate GCF of 42,12,878

Greatest Common Factor (GCF) of 42,12,878 By Common Division

2	42, 12, 878
	21, 6, 439

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

Greatest Common Factor of 42,12,878 By Matching Biggest Common Factor Method

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Now, list down the factors of 12

1,2,3,4,6,12

Now, list down the factors of 878

1,2,439,878

Greatest Common Factor

We found the factors 42,12,878 . The biggest common factor number is the GCF number.
So the greatest common factor 42,12,878 is 2.

Lets's calculate LCM of 70,43,411

Lowest Common Multiple of 70,43,411 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1237110

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1237110

Therefore, the GCF of Fractions 42/70,12/43,878/411 is 2/1237110

Least Common Multiple of 70,43,411 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 70,43,411 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(70,43,411) = 1

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

GCF(70,43,411) x common factors =1 x 1 = 1

LCM(70,43,411) = ( 70 × 43 × 411 ) / 1

LCM(70,43,411) = 1237110 / 1

LCM(70,43,411) = 1237110

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FAQs on GCF of Fractions of 42/70, 12/43, 878/411

1. What is the HCF of 42,12,878?

The HCF of 42,12,878 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 42/70, 12/43, 878/411?

Answer: GCF of Numerators as per given numbers 42/70, 12/43, 878/411 is

GCF of Numerators i.e. for 42,12,878 is 2

LCM of denominators i.e. for 70,43,411 is 1237110.

Thus, GCF of Fractions is 2/1237110.Finally, GCF of Fractions for 42/70, 12/43, 878/411 is 2/1237110.