GCF of 207/57, 322/196
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 207/57, 322/196 i.e 23/11172 easily. The following is the detailed procedure to determine the greatest common factor of fractions 207/57, 322/196.
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 207/57,322/196?
Given fractions are 207/57,322/196
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 207/57,322/196, numerators are 207,322
Denominators are 57,196
The GCF of 207,322 is 23 .
LCM of 57,196 is 11172.
The greatest common factor of 207/57,322/196 = [GCF of 207,322]/[LCM of 57,196]= 23/11172
Therefore, the GCF of 207/57,322/196 is 23/11172.
To find the highest common factor of 207,322, we have to find the factors of both numbers and list the highest common factor.
The factors of 207 are 1, 3, 9, 23, 69, 207
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The HCF of 207,322 is 23.
Lets's calculate GCF of 207,322
| 23 | 207, 322 |
| 9, 14 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 207,322 By Matching Biggest Common Factor Method
Now, list down the factors of 207
:1,3,9,23,69,207
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Greatest Common Factor
We found the factors 207,322 . The biggest common factor number is the GCF number.
So the greatest common factor 207,322 is 23.
Lets's calculate LCM of 57,196
Given numbers has no common factors except 1. So, there LCM is their product i.e 11172
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/11172
Therefore, the GCF of Fractions 207/57,322/196 is 23/11172
Least Common Multiple of 57,196 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 57,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,196) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(57,196) x common factors =1 x 1 = 1
LCM(57,196) = ( 57 × 196 ) / 1
LCM(57,196) = 11172 / 1
LCM(57,196) = 11172
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FAQs on GCF of Fractions of 207/57, 322/196
1. What is the HCF of 207,322?
The HCF of 207,322 is 23
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 207/57, 322/196?
Answer: GCF of Numerators as per given numbers 207/57, 322/196 is
GCF of Numerators i.e. for 207,322 is 23
LCM of denominators i.e. for 57,196 is 11172.
Thus, GCF of Fractions is 23/11172.Finally, GCF of Fractions for 207/57, 322/196 is 23/11172.