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GCF of 689/25, 590/401

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 689/25, 590/401 i.e 1/10025 easily. The following is the detailed procedure to determine the greatest common factor of fractions 689/25, 590/401.

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 689/25,590/401?

Given fractions are 689/25,590/401

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 689/25,590/401, numerators are 689,590

Denominators are 25,401

The GCF of 689,590 is 1 .

LCM of 25,401 is 10025.

The greatest common factor of 689/25,590/401 = [GCF of 689,590]/[LCM of 25,401]= 1/10025

Therefore, the GCF of 689/25,590/401 is 1/10025.

Greatest Common Factor of 689,590

To find the highest common factor of 689,590, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590

The HCF of 689,590 is 1.

Lets's calculate GCF of 689,590

Greatest Common Factor (GCF) of 689,590 By Common Division

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

Greatest Common Factor of 689,590 By Matching Biggest Common Factor Method

Greatest Common Factor of 689,590 By Matching Biggest Common Factor Method

Now, list down the factors of 689

:

1,13,53,689

Now, list down the factors of 590

:

1,2,5,10,59,118,295,590

Greatest Common Factor

We found the factors 689,590 . The biggest common factor number is the GCF number.
So the greatest common factor 689,590 is 1.

Lets's calculate LCM of 25,401

Lowest Common Multiple of 25,401 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 10025

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10025

Therefore, the GCF of Fractions 689/25,590/401 is 1/10025

Least Common Multiple of 25,401 with GCF Formula

Least Common Multiple of 25,401 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 25,401 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(25,401) = 1

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

GCF(25,401) x common factors =1 x 1 = 1

LCM(25,401) = ( 25 × 401 ) / 1

LCM(25,401) = 10025 / 1

LCM(25,401) = 10025


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FAQs on GCF of Fractions of 689/25, 590/401

1. What is the HCF of 689,590?

The HCF of 689,590 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 689/25, 590/401?

Answer: GCF of Numerators as per given numbers 689/25, 590/401 is

GCF of Numerators i.e. for 689,590 is 1

LCM of denominators i.e. for 25,401 is 10025.

Thus, GCF of Fractions is 1/10025.Finally, GCF of Fractions for 689/25, 590/401 is 1/10025.