GCF of 4/65, 17/42, 53/624, 278/161
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4/65, 17/42, 53/624, 278/161 i.e 1/502320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4/65, 17/42, 53/624, 278/161.
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 4/65,17/42,53/624,278/161?
Given fractions are 4/65,17/42,53/624,278/161
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 4/65,17/42,53/624,278/161, numerators are 4,17,53,278
Denominators are 65,42,624,161
The GCF of 4,17,53,278 is 1 .
LCM of 65,42,624,161 is 502320.
The greatest common factor of 4/65,17/42,53/624,278/161 = [GCF of 4,17,53,278]/[LCM of 65,42,624,161]= 1/502320
Therefore, the GCF of 4/65,17/42,53/624,278/161 is 1/502320.
To find the highest common factor of 4,17,53,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 4 are 1, 2, 4
The factors of 17 are 1, 17
The factors of 53 are 1, 53
The factors of 278 are 1, 2, 139, 278
The HCF of 4,17,53,278 is 1.
Lets's calculate GCF of 4,17,53,278
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 4,17,53,278 By Matching Biggest Common Factor Method
Now, list down the factors of 4
:1,2,4
Now, list down the factors of 17
:1,17
Now, list down the factors of 53
:1,53
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 4,17,53,278 . The biggest common factor number is the GCF number.
So the greatest common factor 4,17,53,278 is 1.
Lets's calculate LCM of 65,42,624,161
| 2 | 65, 42, 624, 161 |
| 3 | 65, 21, 312, 161 |
| 7 | 65, 7, 104, 161 |
| 13 | 65, 1, 104, 23 |
| 5, 1, 8, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 13 x 5 x 1 x 8 x 23 = 502320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/502320
Therefore, the GCF of Fractions 4/65,17/42,53/624,278/161 is 1/502320
Least Common Multiple of 65,42,624,161 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 65,42,624,161 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,42,624,161) = 1
common factors(in case of two or more numbers have common factors) = 546
GCF(65,42,624,161) x common factors =1 x 546 = 546
LCM(65,42,624,161) = ( 65 × 42 × 624 × 161 ) / 546
LCM(65,42,624,161) = 274266720 / 546
LCM(65,42,624,161) = 502320
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 4/65, 17/42, 53/624, 278/161
1. What is the HCF of 4,17,53,278?
The HCF of 4,17,53,278 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 4/65, 17/42, 53/624, 278/161?
Answer: GCF of Numerators as per given numbers 4/65, 17/42, 53/624, 278/161 is
GCF of Numerators i.e. for 4,17,53,278 is 1
LCM of denominators i.e. for 65,42,624,161 is 502320.
Thus, GCF of Fractions is 1/502320.Finally, GCF of Fractions for 4/65, 17/42, 53/624, 278/161 is 1/502320.