GCF of 840/30, 264/546
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 840/30, 264/546 i.e 24/2730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 840/30, 264/546.
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 840/30,264/546?
Given fractions are 840/30,264/546
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 840/30,264/546, numerators are 840,264
Denominators are 30,546
The GCF of 840,264 is 24 .
LCM of 30,546 is 2730.
The greatest common factor of 840/30,264/546 = [GCF of 840,264]/[LCM of 30,546]= 24/2730
Therefore, the GCF of 840/30,264/546 is 24/2730.
To find the highest common factor of 840,264, we have to find the factors of both numbers and list the highest common factor.
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264
The HCF of 840,264 is 24.
Lets's calculate GCF of 840,264
| 2 | 840, 264 |
| 2 | 420, 132 |
| 2 | 210, 66 |
| 3 | 105, 33 |
| 35, 11 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 840,264 By Matching Biggest Common Factor Method
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Now, list down the factors of 264
:1,2,3,4,6,8,11,12,22,24,33,44,66,88,132,264
Greatest Common Factor
We found the factors 840,264 . The biggest common factor number is the GCF number.
So the greatest common factor 840,264 is 24.
Lets's calculate LCM of 30,546
| 2 | 30, 546 |
| 3 | 15, 273 |
| 5, 91 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 91 = 2730
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/2730
Therefore, the GCF of Fractions 840/30,264/546 is 24/2730
Least Common Multiple of 30,546 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 30,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,546) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(30,546) x common factors =6 x 1 = 6
LCM(30,546) = ( 30 × 546 ) / 6
LCM(30,546) = 16380 / 6
LCM(30,546) = 2730
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FAQs on GCF of Fractions of 840/30, 264/546
1. What is the HCF of 840,264?
The HCF of 840,264 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 840/30, 264/546?
Answer: GCF of Numerators as per given numbers 840/30, 264/546 is
GCF of Numerators i.e. for 840,264 is 24
LCM of denominators i.e. for 30,546 is 2730.
Thus, GCF of Fractions is 24/2730.Finally, GCF of Fractions for 840/30, 264/546 is 24/2730.