Highest Common Factor of 403, 689, 784 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 403, 689, 784 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 403, 689, 784 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 403, 689, 784 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 403, 689, 784 is 1.

HCF(403, 689, 784) = 1

HCF of 403, 689, 784 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 403, 689, 784 is 1.

Highest Common Factor of 403,689,784 using Euclid's algorithm

Highest Common Factor of 403,689,784 is 1

Step 1: Since 689 > 403, we apply the division lemma to 689 and 403, to get

689 = 403 x 1 + 286

Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 286 and 403, to get

403 = 286 x 1 + 117

Step 3: We consider the new divisor 286 and the new remainder 117, and apply the division lemma to get

286 = 117 x 2 + 52

We consider the new divisor 117 and the new remainder 52,and apply the division lemma to get

117 = 52 x 2 + 13

We consider the new divisor 52 and the new remainder 13,and apply the division lemma to get

52 = 13 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 403 and 689 is 13

Notice that 13 = HCF(52,13) = HCF(117,52) = HCF(286,117) = HCF(403,286) = HCF(689,403) .

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

Step 1: Since 784 > 13, we apply the division lemma to 784 and 13, to get

784 = 13 x 60 + 4

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 4 and 13, to get

13 = 4 x 3 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 784 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(784,13) .

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Frequently Asked Questions on HCF of 403, 689, 784 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 403, 689, 784?

Answer: HCF of 403, 689, 784 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 403, 689, 784 using Euclid's Algorithm?

Answer: For arbitrary numbers 403, 689, 784 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.