How to Find GCF of 364/342, 630/513?

GCF of 364/342, 630/513

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 364/342, 630/513 i.e 14/1026 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/342, 630/513.

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 364/342,630/513?

Given fractions are 364/342,630/513

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 364/342,630/513, numerators are 364,630

Denominators are 342,513

The GCF of 364,630 is 14 .

LCM of 342,513 is 1026.

The greatest common factor of 364/342,630/513 = [GCF of 364,630]/[LCM of 342,513]= 14/1026

Therefore, the GCF of 364/342,630/513 is 14/1026.

Greatest Common Factor of 364,630

To find the highest common factor of 364,630, we have to find the factors of both numbers and list the highest common factor.

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364

The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630

The HCF of 364,630 is 14.

Lets's calculate GCF of 364,630

Greatest Common Factor (GCF) of 364,630 By Common Division

2	364, 630
7	182, 315
	26, 45

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 364,630 By Matching Biggest Common Factor Method

Now, list down the factors of 364

1,2,4,7,13,14,26,28,52,91,182,364

Now, list down the factors of 630

1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630

Greatest Common Factor

We found the factors 364,630 . The biggest common factor number is the GCF number.
So the greatest common factor 364,630 is 14.

Lets's calculate LCM of 342,513

Lowest Common Multiple of 342,513 using Common Division

3	342, 513
3	114, 171
19	38, 57
	2, 3

∴ So the LCM of the given numbers is 3 x 3 x 19 x 2 x 3 = 1026

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1026

Therefore, the GCF of Fractions 364/342,630/513 is 14/1026

Least Common Multiple of 342,513 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 342,513 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(342,513) = 171

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

GCF(342,513) x common factors =171 x 1 = 171

LCM(342,513) = ( 342 × 513 ) / 171

LCM(342,513) = 175446 / 171

LCM(342,513) = 1026

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FAQs on GCF of Fractions of 364/342, 630/513

1. What is the HCF of 364,630?

The HCF of 364,630 is 14

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 364/342, 630/513?

Answer: GCF of Numerators as per given numbers 364/342, 630/513 is

GCF of Numerators i.e. for 364,630 is 14

LCM of denominators i.e. for 342,513 is 1026.

Thus, GCF of Fractions is 14/1026.Finally, GCF of Fractions for 364/342, 630/513 is 14/1026.