Highest Common Factor of 400, 7417, 7443 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 400, 7417, 7443 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 400, 7417, 7443 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 400, 7417, 7443 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 400, 7417, 7443 is 1.

HCF(400, 7417, 7443) = 1

HCF of 400, 7417, 7443 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 400, 7417, 7443 is 1.

Highest Common Factor of 400,7417,7443 using Euclid's algorithm

Highest Common Factor of 400,7417,7443 is 1

Step 1: Since 7417 > 400, we apply the division lemma to 7417 and 400, to get

7417 = 400 x 18 + 217

Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 217 and 400, to get

400 = 217 x 1 + 183

Step 3: We consider the new divisor 217 and the new remainder 183, and apply the division lemma to get

217 = 183 x 1 + 34

We consider the new divisor 183 and the new remainder 34,and apply the division lemma to get

183 = 34 x 5 + 13

We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get

34 = 13 x 2 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 400 and 7417 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(183,34) = HCF(217,183) = HCF(400,217) = HCF(7417,400) .

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

Step 1: Since 7443 > 1, we apply the division lemma to 7443 and 1, to get

7443 = 1 x 7443 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7443 is 1

Notice that 1 = HCF(7443,1) .

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Frequently Asked Questions on HCF of 400, 7417, 7443 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 400, 7417, 7443?

Answer: HCF of 400, 7417, 7443 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 400, 7417, 7443 using Euclid's Algorithm?

Answer: For arbitrary numbers 400, 7417, 7443 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.