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GCF of 653/414, 770/462

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 653/414, 770/462 i.e 1/31878 easily. The following is the detailed procedure to determine the greatest common factor of fractions 653/414, 770/462.

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 653/414,770/462?

Given fractions are 653/414,770/462

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 653/414,770/462, numerators are 653,770

Denominators are 414,462

The GCF of 653,770 is 1 .

LCM of 414,462 is 31878.

The greatest common factor of 653/414,770/462 = [GCF of 653,770]/[LCM of 414,462]= 1/31878

Therefore, the GCF of 653/414,770/462 is 1/31878.

Greatest Common Factor of 653,770

To find the highest common factor of 653,770, we have to find the factors of both numbers and list the highest common factor.

The factors of 653 are 1, 653

The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

The HCF of 653,770 is 1.

Lets's calculate GCF of 653,770

Greatest Common Factor (GCF) of 653,770 By Common Division

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

Greatest Common Factor of 653,770 By Matching Biggest Common Factor Method

Greatest Common Factor of 653,770 By Matching Biggest Common Factor Method

Now, list down the factors of 653

:

1,653

Now, list down the factors of 770

:

1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770

Greatest Common Factor

We found the factors 653,770 . The biggest common factor number is the GCF number.
So the greatest common factor 653,770 is 1.

Lets's calculate LCM of 414,462

Lowest Common Multiple of 414,462 using Common Division

2 414, 462
3 207, 231
69, 77

∴ So the LCM of the given numbers is 2 x 3 x 69 x 77 = 31878

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31878

Therefore, the GCF of Fractions 653/414,770/462 is 1/31878

Least Common Multiple of 414,462 with GCF Formula

Least Common Multiple of 414,462 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 414,462 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(414,462) = 6

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

GCF(414,462) x common factors =6 x 1 = 6

LCM(414,462) = ( 414 × 462 ) / 6

LCM(414,462) = 191268 / 6

LCM(414,462) = 31878


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FAQs on GCF of Fractions of 653/414, 770/462

1. What is the HCF of 653,770?

The HCF of 653,770 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 653/414, 770/462?

Answer: GCF of Numerators as per given numbers 653/414, 770/462 is

GCF of Numerators i.e. for 653,770 is 1

LCM of denominators i.e. for 414,462 is 31878.

Thus, GCF of Fractions is 1/31878.Finally, GCF of Fractions for 653/414, 770/462 is 1/31878.