How to Find GCF of 648/42, 984/1029?

GCF of 648/42, 984/1029

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 648/42, 984/1029 i.e 24/2058 easily. The following is the detailed procedure to determine the greatest common factor of fractions 648/42, 984/1029.

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 648/42,984/1029?

Given fractions are 648/42,984/1029

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 648/42,984/1029, numerators are 648,984

Denominators are 42,1029

The GCF of 648,984 is 24 .

LCM of 42,1029 is 2058.

The greatest common factor of 648/42,984/1029 = [GCF of 648,984]/[LCM of 42,1029]= 24/2058

Therefore, the GCF of 648/42,984/1029 is 24/2058.

Greatest Common Factor of 648,984

To find the highest common factor of 648,984, we have to find the factors of both numbers and list the highest common factor.

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 factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984

The HCF of 648,984 is 24.

Lets's calculate GCF of 648,984

Greatest Common Factor (GCF) of 648,984 By Common Division

2	648, 984
2	324, 492
2	162, 246
3	81, 123
	27, 41

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

Greatest Common Factor of 648,984 By Matching Biggest Common Factor Method

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

Now, list down the factors of 984

1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984

Greatest Common Factor

We found the factors 648,984 . The biggest common factor number is the GCF number.
So the greatest common factor 648,984 is 24.

Lets's calculate LCM of 42,1029

Lowest Common Multiple of 42,1029 using Common Division

3	42, 1029
7	14, 343
	2, 49

∴ So the LCM of the given numbers is 3 x 7 x 2 x 49 = 2058

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/2058

Therefore, the GCF of Fractions 648/42,984/1029 is 24/2058

Least Common Multiple of 42,1029 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 42,1029 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,1029) = 21

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

GCF(42,1029) x common factors =21 x 1 = 21

LCM(42,1029) = ( 42 × 1029 ) / 21

LCM(42,1029) = 43218 / 21

LCM(42,1029) = 2058

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FAQs on GCF of Fractions of 648/42, 984/1029

1. What is the HCF of 648,984?

The HCF of 648,984 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 648/42, 984/1029?

Answer: GCF of Numerators as per given numbers 648/42, 984/1029 is

GCF of Numerators i.e. for 648,984 is 24

LCM of denominators i.e. for 42,1029 is 2058.

Thus, GCF of Fractions is 24/2058.Finally, GCF of Fractions for 648/42, 984/1029 is 24/2058.