GCF of 514/84, 213/132
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 514/84, 213/132 i.e 1/924 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/84, 213/132.
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 514/84,213/132?
Given fractions are 514/84,213/132
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 514/84,213/132, numerators are 514,213
Denominators are 84,132
The GCF of 514,213 is 1 .
LCM of 84,132 is 924.
The greatest common factor of 514/84,213/132 = [GCF of 514,213]/[LCM of 84,132]= 1/924
Therefore, the GCF of 514/84,213/132 is 1/924.
To find the highest common factor of 514,213, we have to find the factors of both numbers and list the highest common factor.
The factors of 514 are 1, 2, 257, 514
The factors of 213 are 1, 3, 71, 213
The HCF of 514,213 is 1.
Lets's calculate GCF of 514,213
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 514,213 By Matching Biggest Common Factor Method
Now, list down the factors of 514
:1,2,257,514
Now, list down the factors of 213
:1,3,71,213
Greatest Common Factor
We found the factors 514,213 . The biggest common factor number is the GCF number.
So the greatest common factor 514,213 is 1.
Lets's calculate LCM of 84,132
| 2 | 84, 132 |
| 2 | 42, 66 |
| 3 | 21, 33 |
| 7, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 11 = 924
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/924
Therefore, the GCF of Fractions 514/84,213/132 is 1/924
Least Common Multiple of 84,132 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 84,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,132) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(84,132) x common factors =12 x 1 = 12
LCM(84,132) = ( 84 × 132 ) / 12
LCM(84,132) = 11088 / 12
LCM(84,132) = 924
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FAQs on GCF of Fractions of 514/84, 213/132
1. What is the HCF of 514,213?
The HCF of 514,213 is 1
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 514/84, 213/132?
Answer: GCF of Numerators as per given numbers 514/84, 213/132 is
GCF of Numerators i.e. for 514,213 is 1
LCM of denominators i.e. for 84,132 is 924.
Thus, GCF of Fractions is 1/924.Finally, GCF of Fractions for 514/84, 213/132 is 1/924.