How to Find GCF of 697/416, 2124/604?

GCF of 697/416, 2124/604

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 697/416, 2124/604 i.e 1/62816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 697/416, 2124/604.

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 697/416,2124/604?

Given fractions are 697/416,2124/604

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 697/416,2124/604, numerators are 697,2124

Denominators are 416,604

The GCF of 697,2124 is 1 .

LCM of 416,604 is 62816.

The greatest common factor of 697/416,2124/604 = [GCF of 697,2124]/[LCM of 416,604]= 1/62816

Therefore, the GCF of 697/416,2124/604 is 1/62816.

Greatest Common Factor of 697,2124

To find the highest common factor of 697,2124, we have to find the factors of both numbers and list the highest common factor.

The factors of 697 are 1, 17, 41, 697

The factors of 2124 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 59, 118, 177, 236, 354, 531, 708, 1062, 2124

The HCF of 697,2124 is 1.

Lets's calculate GCF of 697,2124

Greatest Common Factor (GCF) of 697,2124 By Common Division

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

Greatest Common Factor of 697,2124 By Matching Biggest Common Factor Method

Now, list down the factors of 697

1,17,41,697

Now, list down the factors of 2124

1,2,3,4,6,9,12,18,36,59,118,177,236,354,531,708,1062,2124

Greatest Common Factor

We found the factors 697,2124 . The biggest common factor number is the GCF number.
So the greatest common factor 697,2124 is 1.

Lets's calculate LCM of 416,604

Lowest Common Multiple of 416,604 using Common Division

2	416, 604
2	208, 302
	104, 151

∴ So the LCM of the given numbers is 2 x 2 x 104 x 151 = 62816

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/62816

Therefore, the GCF of Fractions 697/416,2124/604 is 1/62816

Least Common Multiple of 416,604 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 416,604 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(416,604) = 4

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

GCF(416,604) x common factors =4 x 1 = 4

LCM(416,604) = ( 416 × 604 ) / 4

LCM(416,604) = 251264 / 4

LCM(416,604) = 62816

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FAQs on GCF of Fractions of 697/416, 2124/604

1. What is the HCF of 697,2124?

The HCF of 697,2124 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 697/416, 2124/604?

Answer: GCF of Numerators as per given numbers 697/416, 2124/604 is

GCF of Numerators i.e. for 697,2124 is 1

LCM of denominators i.e. for 416,604 is 62816.

Thus, GCF of Fractions is 1/62816.Finally, GCF of Fractions for 697/416, 2124/604 is 1/62816.