How to Find GCF of 252/31, 648/509?

GCF of 252/31, 648/509

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 252/31, 648/509 i.e 36/15779 easily. The following is the detailed procedure to determine the greatest common factor of fractions 252/31, 648/509.

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 252/31,648/509?

Given fractions are 252/31,648/509

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 252/31,648/509, numerators are 252,648

Denominators are 31,509

The GCF of 252,648 is 36 .

LCM of 31,509 is 15779.

The greatest common factor of 252/31,648/509 = [GCF of 252,648]/[LCM of 31,509]= 36/15779

Therefore, the GCF of 252/31,648/509 is 36/15779.

Greatest Common Factor of 252,648

To find the highest common factor of 252,648, we have to find the factors of both numbers and list the highest common factor.

The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

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 252,648 is 36.

Lets's calculate GCF of 252,648

Greatest Common Factor (GCF) of 252,648 By Common Division

2	252, 648
2	126, 324
3	63, 162
3	21, 54
	7, 18

∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36

Greatest Common Factor of 252,648 By Matching Biggest Common Factor Method

Now, list down the factors of 252

1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252

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 252,648 . The biggest common factor number is the GCF number.
So the greatest common factor 252,648 is 36.

Lets's calculate LCM of 31,509

Lowest Common Multiple of 31,509 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 15779

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/15779

Therefore, the GCF of Fractions 252/31,648/509 is 36/15779

Least Common Multiple of 31,509 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 31,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,509) = 1

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

GCF(31,509) x common factors =1 x 1 = 1

LCM(31,509) = ( 31 × 509 ) / 1

LCM(31,509) = 15779 / 1

LCM(31,509) = 15779

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FAQs on GCF of Fractions of 252/31, 648/509

1. What is the HCF of 252,648?

The HCF of 252,648 is 36

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 252/31, 648/509?

Answer: GCF of Numerators as per given numbers 252/31, 648/509 is

GCF of Numerators i.e. for 252,648 is 36

LCM of denominators i.e. for 31,509 is 15779.

Thus, GCF of Fractions is 36/15779.Finally, GCF of Fractions for 252/31, 648/509 is 36/15779.