GCF of 80/420, 22/668, 523/749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 80/420, 22/668, 523/749 i.e 1/7504980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 80/420, 22/668, 523/749.
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 80/420,22/668,523/749?
Given fractions are 80/420,22/668,523/749
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 80/420,22/668,523/749, numerators are 80,22,523
Denominators are 420,668,749
The GCF of 80,22,523 is 1 .
LCM of 420,668,749 is 7504980.
The greatest common factor of 80/420,22/668,523/749 = [GCF of 80,22,523]/[LCM of 420,668,749]= 1/7504980
Therefore, the GCF of 80/420,22/668,523/749 is 1/7504980.
To find the highest common factor of 80,22,523, we have to find the factors of both numbers and list the highest common factor.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 22 are 1, 2, 11, 22
The factors of 523 are 1, 523
The HCF of 80,22,523 is 1.
Lets's calculate GCF of 80,22,523
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 80,22,523 By Matching Biggest Common Factor Method
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 22
:1,2,11,22
Now, list down the factors of 523
:1,523
Greatest Common Factor
We found the factors 80,22,523 . The biggest common factor number is the GCF number.
So the greatest common factor 80,22,523 is 1.
Lets's calculate LCM of 420,668,749
| 2 | 420, 668, 749 |
| 2 | 210, 334, 749 |
| 7 | 105, 167, 749 |
| 15, 167, 107 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 15 x 167 x 107 = 7504980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7504980
Therefore, the GCF of Fractions 80/420,22/668,523/749 is 1/7504980
Least Common Multiple of 420,668,749 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 420,668,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,668,749) = 1
common factors(in case of two or more numbers have common factors) = 28
GCF(420,668,749) x common factors =1 x 28 = 28
LCM(420,668,749) = ( 420 × 668 × 749 ) / 28
LCM(420,668,749) = 210139440 / 28
LCM(420,668,749) = 7504980
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FAQs on GCF of Fractions of 80/420, 22/668, 523/749
1. What is the HCF of 80,22,523?
The HCF of 80,22,523 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 80/420, 22/668, 523/749?
Answer: GCF of Numerators as per given numbers 80/420, 22/668, 523/749 is
GCF of Numerators i.e. for 80,22,523 is 1
LCM of denominators i.e. for 420,668,749 is 7504980.
Thus, GCF of Fractions is 1/7504980.Finally, GCF of Fractions for 80/420, 22/668, 523/749 is 1/7504980.