GCF of 672/374, 168/412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 672/374, 168/412 i.e 168/77044 easily. The following is the detailed procedure to determine the greatest common factor of fractions 672/374, 168/412.
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 672/374,168/412?
Given fractions are 672/374,168/412
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 672/374,168/412, numerators are 672,168
Denominators are 374,412
The GCF of 672,168 is 168 .
LCM of 374,412 is 77044.
The greatest common factor of 672/374,168/412 = [GCF of 672,168]/[LCM of 374,412]= 168/77044
Therefore, the GCF of 672/374,168/412 is 168/77044.
To find the highest common factor of 672,168, we have to find the factors of both numbers and list the highest common factor.
The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The HCF of 672,168 is 168.
Lets's calculate GCF of 672,168
| 2 | 672, 168 |
| 2 | 336, 84 |
| 2 | 168, 42 |
| 3 | 84, 21 |
| 7 | 28, 7 |
| 4, 1 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 7 = 168
Greatest Common Factor of 672,168 By Matching Biggest Common Factor Method
Now, list down the factors of 672
:1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Greatest Common Factor
We found the factors 672,168 . The biggest common factor number is the GCF number.
So the greatest common factor 672,168 is 168.
Lets's calculate LCM of 374,412
| 2 | 374, 412 |
| 187, 206 |
∴ So the LCM of the given numbers is 2 x 187 x 206 = 77044
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 168/77044
Therefore, the GCF of Fractions 672/374,168/412 is 168/77044
Least Common Multiple of 374,412 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 374,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(374,412) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(374,412) x common factors =2 x 1 = 2
LCM(374,412) = ( 374 × 412 ) / 2
LCM(374,412) = 154088 / 2
LCM(374,412) = 77044
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FAQs on GCF of Fractions of 672/374, 168/412
1. What is the HCF of 672,168?
The HCF of 672,168 is 168
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 672/374, 168/412?
Answer: GCF of Numerators as per given numbers 672/374, 168/412 is
GCF of Numerators i.e. for 672,168 is 168
LCM of denominators i.e. for 374,412 is 77044.
Thus, GCF of Fractions is 168/77044.Finally, GCF of Fractions for 672/374, 168/412 is 168/77044.