How to Find GCF of 645/680, 5828/8024?

GCF of 645/680, 5828/8024

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 645/680, 5828/8024 i.e 1/40120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 645/680, 5828/8024.

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 645/680,5828/8024?

Given fractions are 645/680,5828/8024

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 645/680,5828/8024, numerators are 645,5828

Denominators are 680,8024

The GCF of 645,5828 is 1 .

LCM of 680,8024 is 40120.

The greatest common factor of 645/680,5828/8024 = [GCF of 645,5828]/[LCM of 680,8024]= 1/40120

Therefore, the GCF of 645/680,5828/8024 is 1/40120.

Greatest Common Factor of 645,5828

To find the highest common factor of 645,5828, we have to find the factors of both numbers and list the highest common factor.

The factors of 645 are 1, 3, 5, 15, 43, 129, 215, 645

The factors of 5828 are 1, 2, 4, 31, 47, 62, 94, 124, 188, 1457, 2914, 5828

The HCF of 645,5828 is 1.

Lets's calculate GCF of 645,5828

Greatest Common Factor (GCF) of 645,5828 By Common Division

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

Greatest Common Factor of 645,5828 By Matching Biggest Common Factor Method

Now, list down the factors of 645

1,3,5,15,43,129,215,645

Now, list down the factors of 5828

1,2,4,31,47,62,94,124,188,1457,2914,5828

Greatest Common Factor

We found the factors 645,5828 . The biggest common factor number is the GCF number.
So the greatest common factor 645,5828 is 1.

Lets's calculate LCM of 680,8024

Lowest Common Multiple of 680,8024 using Common Division

2	680, 8024
2	340, 4012
2	170, 2006
17	85, 1003
	5, 59

∴ So the LCM of the given numbers is 2 x 2 x 2 x 17 x 5 x 59 = 40120

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/40120

Therefore, the GCF of Fractions 645/680,5828/8024 is 1/40120

Least Common Multiple of 680,8024 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 680,8024 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(680,8024) = 136

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

GCF(680,8024) x common factors =136 x 1 = 136

LCM(680,8024) = ( 680 × 8024 ) / 136

LCM(680,8024) = 5456320 / 136

LCM(680,8024) = 40120

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FAQs on GCF of Fractions of 645/680, 5828/8024

1. What is the HCF of 645,5828?

The HCF of 645,5828 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 645/680, 5828/8024?

Answer: GCF of Numerators as per given numbers 645/680, 5828/8024 is

GCF of Numerators i.e. for 645,5828 is 1

LCM of denominators i.e. for 680,8024 is 40120.

Thus, GCF of Fractions is 1/40120.Finally, GCF of Fractions for 645/680, 5828/8024 is 1/40120.