GCF of 7469/282, 7785/3720
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7469/282, 7785/3720 i.e 1/174840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7469/282, 7785/3720.
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 7469/282,7785/3720?
Given fractions are 7469/282,7785/3720
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 7469/282,7785/3720, numerators are 7469,7785
Denominators are 282,3720
The GCF of 7469,7785 is 1 .
LCM of 282,3720 is 174840.
The greatest common factor of 7469/282,7785/3720 = [GCF of 7469,7785]/[LCM of 282,3720]= 1/174840
Therefore, the GCF of 7469/282,7785/3720 is 1/174840.
To find the highest common factor of 7469,7785, we have to find the factors of both numbers and list the highest common factor.
The factors of 7469 are 1, 7, 11, 77, 97, 679, 1067, 7469
The factors of 7785 are 1, 3, 5, 9, 15, 45, 173, 519, 865, 1557, 2595, 7785
The HCF of 7469,7785 is 1.
Lets's calculate GCF of 7469,7785
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7469,7785 By Matching Biggest Common Factor Method
Now, list down the factors of 7469
:1,7,11,77,97,679,1067,7469
Now, list down the factors of 7785
:1,3,5,9,15,45,173,519,865,1557,2595,7785
Greatest Common Factor
We found the factors 7469,7785 . The biggest common factor number is the GCF number.
So the greatest common factor 7469,7785 is 1.
Lets's calculate LCM of 282,3720
| 2 | 282, 3720 |
| 3 | 141, 1860 |
| 47, 620 |
∴ So the LCM of the given numbers is 2 x 3 x 47 x 620 = 174840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/174840
Therefore, the GCF of Fractions 7469/282,7785/3720 is 1/174840
Least Common Multiple of 282,3720 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 282,3720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(282,3720) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(282,3720) x common factors =6 x 1 = 6
LCM(282,3720) = ( 282 × 3720 ) / 6
LCM(282,3720) = 1049040 / 6
LCM(282,3720) = 174840
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FAQs on GCF of Fractions of 7469/282, 7785/3720
1. What is the HCF of 7469,7785?
The HCF of 7469,7785 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 7469/282, 7785/3720?
Answer: GCF of Numerators as per given numbers 7469/282, 7785/3720 is
GCF of Numerators i.e. for 7469,7785 is 1
LCM of denominators i.e. for 282,3720 is 174840.
Thus, GCF of Fractions is 1/174840.Finally, GCF of Fractions for 7469/282, 7785/3720 is 1/174840.