LCM of 3 Numbers Calculator LCM of 4 Numbers Calculator LCM of 5 Numbers Calculator LCD Calculator How to find LCM LCM and HCF Questions Least Common Denominator Calculator Greatest Common Divisor Calculator HCF Calculator HCF of 3 Numbers Calculator HCF of 4 Numbers Calculator GCD Calculator Greatest Common Factor Calculator Least Common Multiple Calculator Common Factors Calculator

GCF of 345/83, 510/658

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 345/83, 510/658 i.e 15/54614 easily. The following is the detailed procedure to determine the greatest common factor of fractions 345/83, 510/658.

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 345/83,510/658?

Given fractions are 345/83,510/658

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 345/83,510/658, numerators are 345,510

Denominators are 83,658

The GCF of 345,510 is 15 .

LCM of 83,658 is 54614.

The greatest common factor of 345/83,510/658 = [GCF of 345,510]/[LCM of 83,658]= 15/54614

Therefore, the GCF of 345/83,510/658 is 15/54614.

Greatest Common Factor of 345,510

To find the highest common factor of 345,510, we have to find the factors of both numbers and list the highest common factor.

The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345

The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510

The HCF of 345,510 is 15.

Lets's calculate GCF of 345,510

Greatest Common Factor (GCF) of 345,510 By Common Division

3 345, 510
5 115, 170
23, 34

∴ So the GCF of the given numbers is 3 x 5 = 15

Greatest Common Factor of 345,510 By Matching Biggest Common Factor Method

Greatest Common Factor of 345,510 By Matching Biggest Common Factor Method

Now, list down the factors of 345

:

1,3,5,15,23,69,115,345

Now, list down the factors of 510

:

1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510

Greatest Common Factor

We found the factors 345,510 . The biggest common factor number is the GCF number.
So the greatest common factor 345,510 is 15.

Lets's calculate LCM of 83,658

Lowest Common Multiple of 83,658 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 54614

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/54614

Therefore, the GCF of Fractions 345/83,510/658 is 15/54614

Least Common Multiple of 83,658 with GCF Formula

Least Common Multiple of 83,658 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 83,658 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(83,658) = 1

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

GCF(83,658) x common factors =1 x 1 = 1

LCM(83,658) = ( 83 × 658 ) / 1

LCM(83,658) = 54614 / 1

LCM(83,658) = 54614


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 345/83, 510/658

1. What is the HCF of 345,510?

The HCF of 345,510 is 15

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 345/83, 510/658?

Answer: GCF of Numerators as per given numbers 345/83, 510/658 is

GCF of Numerators i.e. for 345,510 is 15

LCM of denominators i.e. for 83,658 is 54614.

Thus, GCF of Fractions is 15/54614.Finally, GCF of Fractions for 345/83, 510/658 is 15/54614.