Highest Common Factor of 472, 735, 305 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 472, 735, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 472, 735, 305 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 472, 735, 305 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 472, 735, 305 is 1.

HCF(472, 735, 305) = 1

HCF of 472, 735, 305 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 472, 735, 305 is 1.

Highest Common Factor of 472,735,305 using Euclid's algorithm

Highest Common Factor of 472,735,305 is 1

Step 1: Since 735 > 472, we apply the division lemma to 735 and 472, to get

735 = 472 x 1 + 263

Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 263 and 472, to get

472 = 263 x 1 + 209

Step 3: We consider the new divisor 263 and the new remainder 209, and apply the division lemma to get

263 = 209 x 1 + 54

We consider the new divisor 209 and the new remainder 54,and apply the division lemma to get

209 = 54 x 3 + 47

We consider the new divisor 54 and the new remainder 47,and apply the division lemma to get

54 = 47 x 1 + 7

We consider the new divisor 47 and the new remainder 7,and apply the division lemma to get

47 = 7 x 6 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 472 and 735 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(47,7) = HCF(54,47) = HCF(209,54) = HCF(263,209) = HCF(472,263) = HCF(735,472) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 305 > 1, we apply the division lemma to 305 and 1, to get

305 = 1 x 305 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 305 is 1

Notice that 1 = HCF(305,1) .

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Frequently Asked Questions on HCF of 472, 735, 305 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 472, 735, 305?

Answer: HCF of 472, 735, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 472, 735, 305 using Euclid's Algorithm?

Answer: For arbitrary numbers 472, 735, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.