GCF of 667/45, 213/24, 780/78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 667/45, 213/24, 780/78 i.e 1/4680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 667/45, 213/24, 780/78.
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 667/45,213/24,780/78?
Given fractions are 667/45,213/24,780/78
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 667/45,213/24,780/78, numerators are 667,213,780
Denominators are 45,24,78
The GCF of 667,213,780 is 1 .
LCM of 45,24,78 is 4680.
The greatest common factor of 667/45,213/24,780/78 = [GCF of 667,213,780]/[LCM of 45,24,78]= 1/4680
Therefore, the GCF of 667/45,213/24,780/78 is 1/4680.
To find the highest common factor of 667,213,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 667 are 1, 23, 29, 667
The factors of 213 are 1, 3, 71, 213
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The HCF of 667,213,780 is 1.
Lets's calculate GCF of 667,213,780
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 667,213,780 By Matching Biggest Common Factor Method
Now, list down the factors of 667
:1,23,29,667
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 667,213,780 . The biggest common factor number is the GCF number.
So the greatest common factor 667,213,780 is 1.
Lets's calculate LCM of 45,24,78
| 2 | 45, 24, 78 |
| 3 | 45, 12, 39 |
| 15, 4, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 15 x 4 x 13 = 4680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4680
Therefore, the GCF of Fractions 667/45,213/24,780/78 is 1/4680
Least Common Multiple of 45,24,78 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 45,24,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,24,78) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(45,24,78) x common factors =3 x 6 = 18
LCM(45,24,78) = ( 45 × 24 × 78 ) / 18
LCM(45,24,78) = 84240 / 18
LCM(45,24,78) = 4680
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FAQs on GCF of Fractions of 667/45, 213/24, 780/78
1. What is the HCF of 667,213,780?
The HCF of 667,213,780 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 667/45, 213/24, 780/78?
Answer: GCF of Numerators as per given numbers 667/45, 213/24, 780/78 is
GCF of Numerators i.e. for 667,213,780 is 1
LCM of denominators i.e. for 45,24,78 is 4680.
Thus, GCF of Fractions is 1/4680.Finally, GCF of Fractions for 667/45, 213/24, 780/78 is 1/4680.