How to Find GCF of 416/171, 677/698?

GCF of 416/171, 677/698

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 416/171, 677/698 i.e 1/119358 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/171, 677/698.

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 416/171,677/698?

Given fractions are 416/171,677/698

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 416/171,677/698, numerators are 416,677

Denominators are 171,698

The GCF of 416,677 is 1 .

LCM of 171,698 is 119358.

The greatest common factor of 416/171,677/698 = [GCF of 416,677]/[LCM of 171,698]= 1/119358

Therefore, the GCF of 416/171,677/698 is 1/119358.

Greatest Common Factor of 416,677

To find the highest common factor of 416,677, 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 677 are 1, 677

The HCF of 416,677 is 1.

Lets's calculate GCF of 416,677

Greatest Common Factor (GCF) of 416,677 By Common Division

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

Greatest Common Factor of 416,677 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 677

1,677

Greatest Common Factor

We found the factors 416,677 . The biggest common factor number is the GCF number.
So the greatest common factor 416,677 is 1.

Lets's calculate LCM of 171,698

Lowest Common Multiple of 171,698 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 119358

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/119358

Therefore, the GCF of Fractions 416/171,677/698 is 1/119358

Least Common Multiple of 171,698 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 171,698 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(171,698) = 1

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

GCF(171,698) x common factors =1 x 1 = 1

LCM(171,698) = ( 171 × 698 ) / 1

LCM(171,698) = 119358 / 1

LCM(171,698) = 119358

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FAQs on GCF of Fractions of 416/171, 677/698

1. What is the HCF of 416,677?

The HCF of 416,677 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 416/171, 677/698?

Answer: GCF of Numerators as per given numbers 416/171, 677/698 is

GCF of Numerators i.e. for 416,677 is 1

LCM of denominators i.e. for 171,698 is 119358.

Thus, GCF of Fractions is 1/119358.Finally, GCF of Fractions for 416/171, 677/698 is 1/119358.