GCF of 410/74, 133/30, 456/67
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 410/74, 133/30, 456/67 i.e 1/74370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/74, 133/30, 456/67.
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 410/74,133/30,456/67?
Given fractions are 410/74,133/30,456/67
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 410/74,133/30,456/67, numerators are 410,133,456
Denominators are 74,30,67
The GCF of 410,133,456 is 1 .
LCM of 74,30,67 is 74370.
The greatest common factor of 410/74,133/30,456/67 = [GCF of 410,133,456]/[LCM of 74,30,67]= 1/74370
Therefore, the GCF of 410/74,133/30,456/67 is 1/74370.
To find the highest common factor of 410,133,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 133 are 1, 7, 19, 133
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 410,133,456 is 1.
Lets's calculate GCF of 410,133,456
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 410,133,456 By Matching Biggest Common Factor Method
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 133
:1,7,19,133
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 410,133,456 . The biggest common factor number is the GCF number.
So the greatest common factor 410,133,456 is 1.
Lets's calculate LCM of 74,30,67
| 2 | 74, 30, 67 |
| 37, 15, 67 |
∴ So the LCM of the given numbers is 2 x 37 x 15 x 67 = 74370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/74370
Therefore, the GCF of Fractions 410/74,133/30,456/67 is 1/74370
Least Common Multiple of 74,30,67 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 74,30,67 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,30,67) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(74,30,67) x common factors =1 x 2 = 2
LCM(74,30,67) = ( 74 × 30 × 67 ) / 2
LCM(74,30,67) = 148740 / 2
LCM(74,30,67) = 74370
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FAQs on GCF of Fractions of 410/74, 133/30, 456/67
1. What is the HCF of 410,133,456?
The HCF of 410,133,456 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 410/74, 133/30, 456/67?
Answer: GCF of Numerators as per given numbers 410/74, 133/30, 456/67 is
GCF of Numerators i.e. for 410,133,456 is 1
LCM of denominators i.e. for 74,30,67 is 74370.
Thus, GCF of Fractions is 1/74370.Finally, GCF of Fractions for 410/74, 133/30, 456/67 is 1/74370.