GCF of 76/270, 123/316, 214/565
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 76/270, 123/316, 214/565 i.e 1/4820580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 76/270, 123/316, 214/565.
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 76/270,123/316,214/565?
Given fractions are 76/270,123/316,214/565
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 76/270,123/316,214/565, numerators are 76,123,214
Denominators are 270,316,565
The GCF of 76,123,214 is 1 .
LCM of 270,316,565 is 4820580.
The greatest common factor of 76/270,123/316,214/565 = [GCF of 76,123,214]/[LCM of 270,316,565]= 1/4820580
Therefore, the GCF of 76/270,123/316,214/565 is 1/4820580.
To find the highest common factor of 76,123,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 123 are 1, 3, 41, 123
The factors of 214 are 1, 2, 107, 214
The HCF of 76,123,214 is 1.
Lets's calculate GCF of 76,123,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 76,123,214 By Matching Biggest Common Factor Method
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 123
:1,3,41,123
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 76,123,214 . The biggest common factor number is the GCF number.
So the greatest common factor 76,123,214 is 1.
Lets's calculate LCM of 270,316,565
| 2 | 270, 316, 565 |
| 5 | 135, 158, 565 |
| 27, 158, 113 |
∴ So the LCM of the given numbers is 2 x 5 x 27 x 158 x 113 = 4820580
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4820580
Therefore, the GCF of Fractions 76/270,123/316,214/565 is 1/4820580
Least Common Multiple of 270,316,565 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 270,316,565 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,316,565) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(270,316,565) x common factors =1 x 10 = 10
LCM(270,316,565) = ( 270 × 316 × 565 ) / 10
LCM(270,316,565) = 48205800 / 10
LCM(270,316,565) = 4820580
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FAQs on GCF of Fractions of 76/270, 123/316, 214/565
1. What is the HCF of 76,123,214?
The HCF of 76,123,214 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 76/270, 123/316, 214/565?
Answer: GCF of Numerators as per given numbers 76/270, 123/316, 214/565 is
GCF of Numerators i.e. for 76,123,214 is 1
LCM of denominators i.e. for 270,316,565 is 4820580.
Thus, GCF of Fractions is 1/4820580.Finally, GCF of Fractions for 76/270, 123/316, 214/565 is 1/4820580.