How to Find GCF of 416/232, 4019/968?

GCF of 416/232, 4019/968

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 416/232, 4019/968 i.e 1/28072 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/232, 4019/968.

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 416/232,4019/968?

Given fractions are 416/232,4019/968

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 416/232,4019/968, numerators are 416,4019

Denominators are 232,968

The GCF of 416,4019 is 1 .

LCM of 232,968 is 28072.

The greatest common factor of 416/232,4019/968 = [GCF of 416,4019]/[LCM of 232,968]= 1/28072

Therefore, the GCF of 416/232,4019/968 is 1/28072.

Greatest Common Factor of 416,4019

To find the highest common factor of 416,4019, we have to find the factors of both numbers and list the highest common factor.

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

The factors of 4019 are 1, 4019

The HCF of 416,4019 is 1.

Lets's calculate GCF of 416,4019

Greatest Common Factor (GCF) of 416,4019 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 416,4019 By Matching Biggest Common Factor Method

Now, list down the factors of 416

1,2,4,8,13,16,26,32,52,104,208,416

Now, list down the factors of 4019

1,4019

Greatest Common Factor

We found the factors 416,4019 . The biggest common factor number is the GCF number.
So the greatest common factor 416,4019 is 1.

Lets's calculate LCM of 232,968

Lowest Common Multiple of 232,968 using Common Division

2	232, 968
2	116, 484
2	58, 242
	29, 121

∴ So the LCM of the given numbers is 2 x 2 x 2 x 29 x 121 = 28072

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28072

Therefore, the GCF of Fractions 416/232,4019/968 is 1/28072

Least Common Multiple of 232,968 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 232,968 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(232,968) = 8

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

GCF(232,968) x common factors =8 x 1 = 8

LCM(232,968) = ( 232 × 968 ) / 8

LCM(232,968) = 224576 / 8

LCM(232,968) = 28072

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FAQs on GCF of Fractions of 416/232, 4019/968

1. What is the HCF of 416,4019?

The HCF of 416,4019 is 1

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 416/232, 4019/968?

Answer: GCF of Numerators as per given numbers 416/232, 4019/968 is

GCF of Numerators i.e. for 416,4019 is 1

LCM of denominators i.e. for 232,968 is 28072.

Thus, GCF of Fractions is 1/28072.Finally, GCF of Fractions for 416/232, 4019/968 is 1/28072.