GCF of 70/85, 49/45, 68/49, 91/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/85, 49/45, 68/49, 91/21 i.e 1/37485 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/85, 49/45, 68/49, 91/21.
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 70/85,49/45,68/49,91/21?
Given fractions are 70/85,49/45,68/49,91/21
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 70/85,49/45,68/49,91/21, numerators are 70,49,68,91
Denominators are 85,45,49,21
The GCF of 70,49,68,91 is 1 .
LCM of 85,45,49,21 is 37485.
The greatest common factor of 70/85,49/45,68/49,91/21 = [GCF of 70,49,68,91]/[LCM of 85,45,49,21]= 1/37485
Therefore, the GCF of 70/85,49/45,68/49,91/21 is 1/37485.
To find the highest common factor of 70,49,68,91, we have to find the factors of both numbers and list the highest common factor.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 49 are 1, 7, 49
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 91 are 1, 7, 13, 91
The HCF of 70,49,68,91 is 1.
Lets's calculate GCF of 70,49,68,91
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 70,49,68,91 By Matching Biggest Common Factor Method
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 91
:1,7,13,91
Greatest Common Factor
We found the factors 70,49,68,91 . The biggest common factor number is the GCF number.
So the greatest common factor 70,49,68,91 is 1.
Lets's calculate LCM of 85,45,49,21
| 3 | 85, 45, 49, 21 |
| 5 | 85, 15, 49, 7 |
| 7 | 17, 3, 49, 7 |
| 17, 3, 1, 7 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 17 x 3 x 1 x 7 = 37485
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37485
Therefore, the GCF of Fractions 70/85,49/45,68/49,91/21 is 1/37485
Least Common Multiple of 85,45,49,21 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 85,45,49,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,45,49,21) = 1
common factors(in case of two or more numbers have common factors) = 105
GCF(85,45,49,21) x common factors =1 x 105 = 105
LCM(85,45,49,21) = ( 85 × 45 × 49 × 21 ) / 105
LCM(85,45,49,21) = 3935925 / 105
LCM(85,45,49,21) = 37485
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FAQs on GCF of Fractions of 70/85, 49/45, 68/49, 91/21
1. What is the HCF of 70,49,68,91?
The HCF of 70,49,68,91 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 70/85, 49/45, 68/49, 91/21?
Answer: GCF of Numerators as per given numbers 70/85, 49/45, 68/49, 91/21 is
GCF of Numerators i.e. for 70,49,68,91 is 1
LCM of denominators i.e. for 85,45,49,21 is 37485.
Thus, GCF of Fractions is 1/37485.Finally, GCF of Fractions for 70/85, 49/45, 68/49, 91/21 is 1/37485.