GCF of 348/406, 217/152
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 348/406, 217/152 i.e 1/30856 easily. The following is the detailed procedure to determine the greatest common factor of fractions 348/406, 217/152.
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 348/406,217/152?
Given fractions are 348/406,217/152
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 348/406,217/152, numerators are 348,217
Denominators are 406,152
The GCF of 348,217 is 1 .
LCM of 406,152 is 30856.
The greatest common factor of 348/406,217/152 = [GCF of 348,217]/[LCM of 406,152]= 1/30856
Therefore, the GCF of 348/406,217/152 is 1/30856.
To find the highest common factor of 348,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
The factors of 217 are 1, 7, 31, 217
The HCF of 348,217 is 1.
Lets's calculate GCF of 348,217
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 348,217 By Matching Biggest Common Factor Method
Now, list down the factors of 348
:1,2,3,4,6,12,29,58,87,116,174,348
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 348,217 . The biggest common factor number is the GCF number.
So the greatest common factor 348,217 is 1.
Lets's calculate LCM of 406,152
| 2 | 406, 152 |
| 203, 76 |
∴ So the LCM of the given numbers is 2 x 203 x 76 = 30856
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30856
Therefore, the GCF of Fractions 348/406,217/152 is 1/30856
Least Common Multiple of 406,152 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 406,152 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,152) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(406,152) x common factors =2 x 1 = 2
LCM(406,152) = ( 406 × 152 ) / 2
LCM(406,152) = 61712 / 2
LCM(406,152) = 30856
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FAQs on GCF of Fractions of 348/406, 217/152
1. What is the HCF of 348,217?
The HCF of 348,217 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 348/406, 217/152?
Answer: GCF of Numerators as per given numbers 348/406, 217/152 is
GCF of Numerators i.e. for 348,217 is 1
LCM of denominators i.e. for 406,152 is 30856.
Thus, GCF of Fractions is 1/30856.Finally, GCF of Fractions for 348/406, 217/152 is 1/30856.