How to Find GCF of 336/17, 648/254?

GCF of 336/17, 648/254

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 336/17, 648/254 i.e 24/4318 easily. The following is the detailed procedure to determine the greatest common factor of fractions 336/17, 648/254.

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 336/17,648/254?

Given fractions are 336/17,648/254

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 336/17,648/254, numerators are 336,648

Denominators are 17,254

The GCF of 336,648 is 24 .

LCM of 17,254 is 4318.

The greatest common factor of 336/17,648/254 = [GCF of 336,648]/[LCM of 17,254]= 24/4318

Therefore, the GCF of 336/17,648/254 is 24/4318.

Greatest Common Factor of 336,648

To find the highest common factor of 336,648, we have to find the factors of both numbers and list the highest common factor.

The factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336

The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648

The HCF of 336,648 is 24.

Lets's calculate GCF of 336,648

Greatest Common Factor (GCF) of 336,648 By Common Division

2	336, 648
2	168, 324
2	84, 162
3	42, 81
	14, 27

∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24

Greatest Common Factor of 336,648 By Matching Biggest Common Factor Method

Now, list down the factors of 336

1,2,3,4,6,7,8,12,14,16,21,24,28,42,48,56,84,112,168,336

Now, list down the factors of 648

1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648

Greatest Common Factor

We found the factors 336,648 . The biggest common factor number is the GCF number.
So the greatest common factor 336,648 is 24.

Lets's calculate LCM of 17,254

Lowest Common Multiple of 17,254 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4318

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/4318

Therefore, the GCF of Fractions 336/17,648/254 is 24/4318

Least Common Multiple of 17,254 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 17,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,254) = 1

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

GCF(17,254) x common factors =1 x 1 = 1

LCM(17,254) = ( 17 × 254 ) / 1

LCM(17,254) = 4318 / 1

LCM(17,254) = 4318

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FAQs on GCF of Fractions of 336/17, 648/254

1. What is the HCF of 336,648?

The HCF of 336,648 is 24

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 336/17, 648/254?

Answer: GCF of Numerators as per given numbers 336/17, 648/254 is

GCF of Numerators i.e. for 336,648 is 24

LCM of denominators i.e. for 17,254 is 4318.

Thus, GCF of Fractions is 24/4318.Finally, GCF of Fractions for 336/17, 648/254 is 24/4318.