GCF of 10/34, 84/63, 66/51, 21/66
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 10/34, 84/63, 66/51, 21/66 i.e 1/23562 easily. The following is the detailed procedure to determine the greatest common factor of fractions 10/34, 84/63, 66/51, 21/66.
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 10/34,84/63,66/51,21/66?
Given fractions are 10/34,84/63,66/51,21/66
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 10/34,84/63,66/51,21/66, numerators are 10,84,66,21
Denominators are 34,63,51,66
The GCF of 10,84,66,21 is 1 .
LCM of 34,63,51,66 is 23562.
The greatest common factor of 10/34,84/63,66/51,21/66 = [GCF of 10,84,66,21]/[LCM of 34,63,51,66]= 1/23562
Therefore, the GCF of 10/34,84/63,66/51,21/66 is 1/23562.
To find the highest common factor of 10,84,66,21, we have to find the factors of both numbers and list the highest common factor.
The factors of 10 are 1, 2, 5, 10
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 21 are 1, 3, 7, 21
The HCF of 10,84,66,21 is 1.
Lets's calculate GCF of 10,84,66,21
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 10,84,66,21 By Matching Biggest Common Factor Method
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 21
:1,3,7,21
Greatest Common Factor
We found the factors 10,84,66,21 . The biggest common factor number is the GCF number.
So the greatest common factor 10,84,66,21 is 1.
Lets's calculate LCM of 34,63,51,66
| 2 | 34, 63, 51, 66 |
| 3 | 17, 63, 51, 33 |
| 17 | 17, 21, 17, 11 |
| 1, 21, 1, 11 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 1 x 21 x 1 x 11 = 23562
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23562
Therefore, the GCF of Fractions 10/34,84/63,66/51,21/66 is 1/23562
Least Common Multiple of 34,63,51,66 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 34,63,51,66 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,63,51,66) = 1
common factors(in case of two or more numbers have common factors) = 306
GCF(34,63,51,66) x common factors =1 x 306 = 306
LCM(34,63,51,66) = ( 34 × 63 × 51 × 66 ) / 306
LCM(34,63,51,66) = 7209972 / 306
LCM(34,63,51,66) = 23562
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 10/34, 84/63, 66/51, 21/66
1. What is the HCF of 10,84,66,21?
The HCF of 10,84,66,21 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 10/34, 84/63, 66/51, 21/66?
Answer: GCF of Numerators as per given numbers 10/34, 84/63, 66/51, 21/66 is
GCF of Numerators i.e. for 10,84,66,21 is 1
LCM of denominators i.e. for 34,63,51,66 is 23562.
Thus, GCF of Fractions is 1/23562.Finally, GCF of Fractions for 10/34, 84/63, 66/51, 21/66 is 1/23562.