How to Find GCF of 17/653, 34/320, 391/680?

GCF of 17/653, 34/320, 391/680

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 17/653, 34/320, 391/680 i.e 17/3552320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/653, 34/320, 391/680.

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 17/653,34/320,391/680?

Given fractions are 17/653,34/320,391/680

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 17/653,34/320,391/680, numerators are 17,34,391

Denominators are 653,320,680

The GCF of 17,34,391 is 17 .

LCM of 653,320,680 is 3552320.

The greatest common factor of 17/653,34/320,391/680 = [GCF of 17,34,391]/[LCM of 653,320,680]= 17/3552320

Therefore, the GCF of 17/653,34/320,391/680 is 17/3552320.

Greatest Common Factor of 17,34,391

To find the highest common factor of 17,34,391, we have to find the factors of both numbers and list the highest common factor.

The factors of 17 are 1, 17

The factors of 34 are 1, 2, 17, 34

The factors of 391 are 1, 17, 23, 391

The HCF of 17,34,391 is 17.

Lets's calculate GCF of 17,34,391

Greatest Common Factor (GCF) of 17,34,391 By Common Division

17	17, 34, 391
	1, 2, 23

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 17,34,391 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 391

1,17,23,391

Greatest Common Factor

We found the factors 17,34,391 . The biggest common factor number is the GCF number.
So the greatest common factor 17,34,391 is 17.

Lets's calculate LCM of 653,320,680

Lowest Common Multiple of 653,320,680 using Common Division

2	653, 320, 680
2	653, 160, 340
2	653, 80, 170
5	653, 40, 85
	653, 8, 17

∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 653 x 8 x 17 = 3552320

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/3552320

Therefore, the GCF of Fractions 17/653,34/320,391/680 is 17/3552320

Least Common Multiple of 653,320,680 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 653,320,680 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(653,320,680) = 1

common factors(in case of two or more numbers have common factors) = 40

GCF(653,320,680) x common factors =1 x 40 = 40

LCM(653,320,680) = ( 653 × 320 × 680 ) / 40

LCM(653,320,680) = 142092800 / 40

LCM(653,320,680) = 3552320

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 17/653, 34/320, 391/680

1. What is the HCF of 17,34,391?

The HCF of 17,34,391 is 17

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 17/653, 34/320, 391/680?

Answer: GCF of Numerators as per given numbers 17/653, 34/320, 391/680 is

GCF of Numerators i.e. for 17,34,391 is 17

LCM of denominators i.e. for 653,320,680 is 3552320.

Thus, GCF of Fractions is 17/3552320.Finally, GCF of Fractions for 17/653, 34/320, 391/680 is 17/3552320.