How to Find GCF of 352/23, 416/265?

GCF of 352/23, 416/265

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 352/23, 416/265 i.e 32/6095 easily. The following is the detailed procedure to determine the greatest common factor of fractions 352/23, 416/265.

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 352/23,416/265?

Given fractions are 352/23,416/265

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 352/23,416/265, numerators are 352,416

Denominators are 23,265

The GCF of 352,416 is 32 .

LCM of 23,265 is 6095.

The greatest common factor of 352/23,416/265 = [GCF of 352,416]/[LCM of 23,265]= 32/6095

Therefore, the GCF of 352/23,416/265 is 32/6095.

Greatest Common Factor of 352,416

To find the highest common factor of 352,416, we have to find the factors of both numbers and list the highest common factor.

The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

The HCF of 352,416 is 32.

Lets's calculate GCF of 352,416

Greatest Common Factor (GCF) of 352,416 By Common Division

2	352, 416
2	176, 208
2	88, 104
2	44, 52
2	22, 26
	11, 13

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 352,416 By Matching Biggest Common Factor Method

Now, list down the factors of 352

1,2,4,8,11,16,22,32,44,88,176,352

Now, list down the factors of 416

1,2,4,8,13,16,26,32,52,104,208,416

Greatest Common Factor

We found the factors 352,416 . The biggest common factor number is the GCF number.
So the greatest common factor 352,416 is 32.

Lets's calculate LCM of 23,265

Lowest Common Multiple of 23,265 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 6095

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/6095

Therefore, the GCF of Fractions 352/23,416/265 is 32/6095

Least Common Multiple of 23,265 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 23,265 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,265) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(23,265) x common factors =1 x 1 = 1

LCM(23,265) = ( 23 × 265 ) / 1

LCM(23,265) = 6095 / 1

LCM(23,265) = 6095

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FAQs on GCF of Fractions of 352/23, 416/265

1. What is the HCF of 352,416?

The HCF of 352,416 is 32

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 352/23, 416/265?

Answer: GCF of Numerators as per given numbers 352/23, 416/265 is

GCF of Numerators i.e. for 352,416 is 32

LCM of denominators i.e. for 23,265 is 6095.

Thus, GCF of Fractions is 32/6095.Finally, GCF of Fractions for 352/23, 416/265 is 32/6095.