GCF of 462/640, 672/280
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 462/640, 672/280 i.e 42/4480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/640, 672/280.
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 462/640,672/280?
Given fractions are 462/640,672/280
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 462/640,672/280, numerators are 462,672
Denominators are 640,280
The GCF of 462,672 is 42 .
LCM of 640,280 is 4480.
The greatest common factor of 462/640,672/280 = [GCF of 462,672]/[LCM of 640,280]= 42/4480
Therefore, the GCF of 462/640,672/280 is 42/4480.
To find the highest common factor of 462,672, we have to find the factors of both numbers and list the highest common factor.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672
The HCF of 462,672 is 42.
Lets's calculate GCF of 462,672
| 2 | 462, 672 |
| 3 | 231, 336 |
| 7 | 77, 112 |
| 11, 16 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Greatest Common Factor of 462,672 By Matching Biggest Common Factor Method
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Now, list down the factors of 672
:1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672
Greatest Common Factor
We found the factors 462,672 . The biggest common factor number is the GCF number.
So the greatest common factor 462,672 is 42.
Lets's calculate LCM of 640,280
| 2 | 640, 280 |
| 2 | 320, 140 |
| 2 | 160, 70 |
| 5 | 80, 35 |
| 16, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 16 x 7 = 4480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/4480
Therefore, the GCF of Fractions 462/640,672/280 is 42/4480
Least Common Multiple of 640,280 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 640,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(640,280) = 40
common factors(in case of two or more numbers have common factors) = 1
GCF(640,280) x common factors =40 x 1 = 40
LCM(640,280) = ( 640 × 280 ) / 40
LCM(640,280) = 179200 / 40
LCM(640,280) = 4480
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FAQs on GCF of Fractions of 462/640, 672/280
1. What is the HCF of 462,672?
The HCF of 462,672 is 42
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 462/640, 672/280?
Answer: GCF of Numerators as per given numbers 462/640, 672/280 is
GCF of Numerators i.e. for 462,672 is 42
LCM of denominators i.e. for 640,280 is 4480.
Thus, GCF of Fractions is 42/4480.Finally, GCF of Fractions for 462/640, 672/280 is 42/4480.