GCF of 234/822, 522/148
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 234/822, 522/148 i.e 18/60828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 234/822, 522/148.
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 234/822,522/148?
Given fractions are 234/822,522/148
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 234/822,522/148, numerators are 234,522
Denominators are 822,148
The GCF of 234,522 is 18 .
LCM of 822,148 is 60828.
The greatest common factor of 234/822,522/148 = [GCF of 234,522]/[LCM of 822,148]= 18/60828
Therefore, the GCF of 234/822,522/148 is 18/60828.
To find the highest common factor of 234,522, we have to find the factors of both numbers and list the highest common factor.
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522
The HCF of 234,522 is 18.
Lets's calculate GCF of 234,522
| 2 | 234, 522 |
| 3 | 117, 261 |
| 3 | 39, 87 |
| 13, 29 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 234,522 By Matching Biggest Common Factor Method
Now, list down the factors of 234
:1,2,3,6,9,13,18,26,39,78,117,234
Now, list down the factors of 522
:1,2,3,6,9,18,29,58,87,174,261,522
Greatest Common Factor
We found the factors 234,522 . The biggest common factor number is the GCF number.
So the greatest common factor 234,522 is 18.
Lets's calculate LCM of 822,148
| 2 | 822, 148 |
| 411, 74 |
∴ So the LCM of the given numbers is 2 x 411 x 74 = 60828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/60828
Therefore, the GCF of Fractions 234/822,522/148 is 18/60828
Least Common Multiple of 822,148 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 822,148 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(822,148) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(822,148) x common factors =2 x 1 = 2
LCM(822,148) = ( 822 × 148 ) / 2
LCM(822,148) = 121656 / 2
LCM(822,148) = 60828
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FAQs on GCF of Fractions of 234/822, 522/148
1. What is the HCF of 234,522?
The HCF of 234,522 is 18
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 234/822, 522/148?
Answer: GCF of Numerators as per given numbers 234/822, 522/148 is
GCF of Numerators i.e. for 234,522 is 18
LCM of denominators i.e. for 822,148 is 60828.
Thus, GCF of Fractions is 18/60828.Finally, GCF of Fractions for 234/822, 522/148 is 18/60828.