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GCF of 357/369, 686/700

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 357/369, 686/700 i.e 7/258300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 357/369, 686/700.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 357/369,686/700?

Given fractions are 357/369,686/700

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 357/369,686/700, numerators are 357,686

Denominators are 369,700

The GCF of 357,686 is 7 .

LCM of 369,700 is 258300.

The greatest common factor of 357/369,686/700 = [GCF of 357,686]/[LCM of 369,700]= 7/258300

Therefore, the GCF of 357/369,686/700 is 7/258300.

Greatest Common Factor of 357,686

To find the highest common factor of 357,686, we have to find the factors of both numbers and list the highest common factor.

The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357

The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686

The HCF of 357,686 is 7.

Lets's calculate GCF of 357,686

Greatest Common Factor (GCF) of 357,686 By Common Division

7 357, 686
51, 98

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 357,686 By Matching Biggest Common Factor Method

Greatest Common Factor of 357,686 By Matching Biggest Common Factor Method

Now, list down the factors of 357

:

1,3,7,17,21,51,119,357

Now, list down the factors of 686

:

1,2,7,14,49,98,343,686

Greatest Common Factor

We found the factors 357,686 . The biggest common factor number is the GCF number.
So the greatest common factor 357,686 is 7.

Lets's calculate LCM of 369,700

Lowest Common Multiple of 369,700 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 258300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/258300

Therefore, the GCF of Fractions 357/369,686/700 is 7/258300

Least Common Multiple of 369,700 with GCF Formula

Least Common Multiple of 369,700 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 369,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(369,700) = 1

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

GCF(369,700) x common factors =1 x 1 = 1

LCM(369,700) = ( 369 × 700 ) / 1

LCM(369,700) = 258300 / 1

LCM(369,700) = 258300


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FAQs on GCF of Fractions of 357/369, 686/700

1. What is the HCF of 357,686?

The HCF of 357,686 is 7

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 357/369, 686/700?

Answer: GCF of Numerators as per given numbers 357/369, 686/700 is

GCF of Numerators i.e. for 357,686 is 7

LCM of denominators i.e. for 369,700 is 258300.

Thus, GCF of Fractions is 7/258300.Finally, GCF of Fractions for 357/369, 686/700 is 7/258300.