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GCF of 34/578, 53/6970

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 34/578, 53/6970 i.e 1/118490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/578, 53/6970.

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 34/578,53/6970?

Given fractions are 34/578,53/6970

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 34/578,53/6970, numerators are 34,53

Denominators are 578,6970

The GCF of 34,53 is 1 .

LCM of 578,6970 is 118490.

The greatest common factor of 34/578,53/6970 = [GCF of 34,53]/[LCM of 578,6970]= 1/118490

Therefore, the GCF of 34/578,53/6970 is 1/118490.

Greatest Common Factor of 34,53

To find the highest common factor of 34,53, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 53 are 1, 53

The HCF of 34,53 is 1.

Lets's calculate GCF of 34,53

Greatest Common Factor (GCF) of 34,53 By Common Division

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

Greatest Common Factor of 34,53 By Matching Biggest Common Factor Method

Greatest Common Factor of 34,53 By Matching Biggest Common Factor Method

Now, list down the factors of 34

:

1,2,17,34

Now, list down the factors of 53

:

1,53

Greatest Common Factor

We found the factors 34,53 . The biggest common factor number is the GCF number.
So the greatest common factor 34,53 is 1.

Lets's calculate LCM of 578,6970

Lowest Common Multiple of 578,6970 using Common Division

2 578, 6970
17 289, 3485
17, 205

∴ So the LCM of the given numbers is 2 x 17 x 17 x 205 = 118490

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/118490

Therefore, the GCF of Fractions 34/578,53/6970 is 1/118490

Least Common Multiple of 578,6970 with GCF Formula

Least Common Multiple of 578,6970 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 578,6970 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(578,6970) = 34

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

GCF(578,6970) x common factors =34 x 1 = 34

LCM(578,6970) = ( 578 × 6970 ) / 34

LCM(578,6970) = 4028660 / 34

LCM(578,6970) = 118490


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FAQs on GCF of Fractions of 34/578, 53/6970

1. What is the HCF of 34,53?

The HCF of 34,53 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 34/578, 53/6970?

Answer: GCF of Numerators as per given numbers 34/578, 53/6970 is

GCF of Numerators i.e. for 34,53 is 1

LCM of denominators i.e. for 578,6970 is 118490.

Thus, GCF of Fractions is 1/118490.Finally, GCF of Fractions for 34/578, 53/6970 is 1/118490.