GCF of 214/32, 416/114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 214/32, 416/114 i.e 2/1824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 214/32, 416/114.
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 214/32,416/114?
Given fractions are 214/32,416/114
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 214/32,416/114, numerators are 214,416
Denominators are 32,114
The GCF of 214,416 is 2 .
LCM of 32,114 is 1824.
The greatest common factor of 214/32,416/114 = [GCF of 214,416]/[LCM of 32,114]= 2/1824
Therefore, the GCF of 214/32,416/114 is 2/1824.
To find the highest common factor of 214,416, we have to find the factors of both numbers and list the highest common factor.
The factors of 214 are 1, 2, 107, 214
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The HCF of 214,416 is 2.
Lets's calculate GCF of 214,416
| 2 | 214, 416 |
| 107, 208 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 214,416 By Matching Biggest Common Factor Method
Now, list down the factors of 214
:1,2,107,214
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 214,416 . The biggest common factor number is the GCF number.
So the greatest common factor 214,416 is 2.
Lets's calculate LCM of 32,114
| 2 | 32, 114 |
| 16, 57 |
∴ So the LCM of the given numbers is 2 x 16 x 57 = 1824
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1824
Therefore, the GCF of Fractions 214/32,416/114 is 2/1824
Least Common Multiple of 32,114 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 32,114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,114) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,114) x common factors =2 x 1 = 2
LCM(32,114) = ( 32 × 114 ) / 2
LCM(32,114) = 3648 / 2
LCM(32,114) = 1824
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FAQs on GCF of Fractions of 214/32, 416/114
1. What is the HCF of 214,416?
The HCF of 214,416 is 2
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 214/32, 416/114?
Answer: GCF of Numerators as per given numbers 214/32, 416/114 is
GCF of Numerators i.e. for 214,416 is 2
LCM of denominators i.e. for 32,114 is 1824.
Thus, GCF of Fractions is 2/1824.Finally, GCF of Fractions for 214/32, 416/114 is 2/1824.