How to Find GCF of 35/58, 449/60, 689/984?

GCF of 35/58, 449/60, 689/984

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 35/58, 449/60, 689/984 i.e 1/142680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/58, 449/60, 689/984.

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 35/58,449/60,689/984?

Given fractions are 35/58,449/60,689/984

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 35/58,449/60,689/984, numerators are 35,449,689

Denominators are 58,60,984

The GCF of 35,449,689 is 1 .

LCM of 58,60,984 is 142680.

The greatest common factor of 35/58,449/60,689/984 = [GCF of 35,449,689]/[LCM of 58,60,984]= 1/142680

Therefore, the GCF of 35/58,449/60,689/984 is 1/142680.

Greatest Common Factor of 35,449,689

To find the highest common factor of 35,449,689, we have to find the factors of both numbers and list the highest common factor.

The factors of 35 are 1, 5, 7, 35

The factors of 449 are 1, 449

The factors of 689 are 1, 13, 53, 689

The HCF of 35,449,689 is 1.

Lets's calculate GCF of 35,449,689

Greatest Common Factor (GCF) of 35,449,689 By Common Division

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

Greatest Common Factor of 35,449,689 By Matching Biggest Common Factor Method

Now, list down the factors of 35

1,5,7,35

Now, list down the factors of 449

1,449

Now, list down the factors of 689

1,13,53,689

Greatest Common Factor

We found the factors 35,449,689 . The biggest common factor number is the GCF number.
So the greatest common factor 35,449,689 is 1.

Lets's calculate LCM of 58,60,984

Lowest Common Multiple of 58,60,984 using Common Division

2	58, 60, 984
2	29, 30, 492
3	29, 15, 246
	29, 5, 82

∴ So the LCM of the given numbers is 2 x 2 x 3 x 29 x 5 x 82 = 142680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/142680

Therefore, the GCF of Fractions 35/58,449/60,689/984 is 1/142680

Least Common Multiple of 58,60,984 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 58,60,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(58,60,984) = 2

common factors(in case of two or more numbers have common factors) = 12

GCF(58,60,984) x common factors =2 x 12 = 24

LCM(58,60,984) = ( 58 × 60 × 984 ) / 24

LCM(58,60,984) = 3424320 / 24

LCM(58,60,984) = 142680

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 35/58, 449/60, 689/984

1. What is the HCF of 35,449,689?

The HCF of 35,449,689 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 35/58, 449/60, 689/984?

Answer: GCF of Numerators as per given numbers 35/58, 449/60, 689/984 is

GCF of Numerators i.e. for 35,449,689 is 1

LCM of denominators i.e. for 58,60,984 is 142680.

Thus, GCF of Fractions is 1/142680.Finally, GCF of Fractions for 35/58, 449/60, 689/984 is 1/142680.