GCF of 46/70, 854/14, 967/196
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 46/70, 854/14, 967/196 i.e 1/980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/70, 854/14, 967/196.
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 46/70,854/14,967/196?
Given fractions are 46/70,854/14,967/196
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 46/70,854/14,967/196, numerators are 46,854,967
Denominators are 70,14,196
The GCF of 46,854,967 is 1 .
LCM of 70,14,196 is 980.
The greatest common factor of 46/70,854/14,967/196 = [GCF of 46,854,967]/[LCM of 70,14,196]= 1/980
Therefore, the GCF of 46/70,854/14,967/196 is 1/980.
To find the highest common factor of 46,854,967, we have to find the factors of both numbers and list the highest common factor.
The factors of 46 are 1, 2, 23, 46
The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854
The factors of 967 are 1, 967
The HCF of 46,854,967 is 1.
Lets's calculate GCF of 46,854,967
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 46,854,967 By Matching Biggest Common Factor Method
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 854
:1,2,7,14,61,122,427,854
Now, list down the factors of 967
:1,967
Greatest Common Factor
We found the factors 46,854,967 . The biggest common factor number is the GCF number.
So the greatest common factor 46,854,967 is 1.
Lets's calculate LCM of 70,14,196
| 2 | 70, 14, 196 |
| 7 | 35, 7, 98 |
| 5, 1, 14 |
∴ So the LCM of the given numbers is 2 x 7 x 5 x 1 x 14 = 980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/980
Therefore, the GCF of Fractions 46/70,854/14,967/196 is 1/980
Least Common Multiple of 70,14,196 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 70,14,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,14,196) = 14
common factors(in case of two or more numbers have common factors) = 14
GCF(70,14,196) x common factors =14 x 14 = 196
LCM(70,14,196) = ( 70 × 14 × 196 ) / 196
LCM(70,14,196) = 192080 / 196
LCM(70,14,196) = 980
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FAQs on GCF of Fractions of 46/70, 854/14, 967/196
1. What is the HCF of 46,854,967?
The HCF of 46,854,967 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 46/70, 854/14, 967/196?
Answer: GCF of Numerators as per given numbers 46/70, 854/14, 967/196 is
GCF of Numerators i.e. for 46,854,967 is 1
LCM of denominators i.e. for 70,14,196 is 980.
Thus, GCF of Fractions is 1/980.Finally, GCF of Fractions for 46/70, 854/14, 967/196 is 1/980.