Use our free GCF of Fractions Calculator tool to compute the GCF of 456/316, 688/149 i.e 8/47084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 456/316, 688/149.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 456/316,688/149
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 456/316,688/149, numerators are 456,688
Denominators are 316,149
The GCF of 456,688 is 8 .
LCM of 316,149 is 47084.
The greatest common factor of 456/316,688/149 = [GCF of 456,688]/[LCM of 316,149]= 8/47084
Therefore, the GCF of 456/316,688/149 is 8/47084.
To find the highest common factor of 456,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 456,688 is 8.
Lets's calculate GCF of 456,688
2 | 456, 688 |
2 | 228, 344 |
2 | 114, 172 |
57, 86 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 456,688 . The biggest common factor number is the GCF number.
So the greatest common factor 456,688 is 8.
Lets's calculate LCM of 316,149
Given numbers has no common factors except 1. So, there LCM is their product i.e 47084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/47084
Therefore, the GCF of Fractions 456/316,688/149 is 8/47084
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 316,149 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(316,149) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(316,149) x common factors =1 x 1 = 1
LCM(316,149) = ( 316 × 149 ) / 1
LCM(316,149) = 47084 / 1
LCM(316,149) = 47084
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 456,688?
The HCF of 456,688 is 8
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 456/316, 688/149?
Answer: GCF of Numerators as per given numbers 456/316, 688/149 is
GCF of Numerators i.e. for 456,688 is 8
LCM of denominators i.e. for 316,149 is 47084.
Thus, GCF of Fractions is 8/47084.Finally, GCF of Fractions for 456/316, 688/149 is 8/47084.