Highest Common Factor of 406, 630, 685 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 406, 630, 685 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 406, 630, 685 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 406, 630, 685 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 406, 630, 685 is 1.

HCF(406, 630, 685) = 1

HCF of 406, 630, 685 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 406, 630, 685 is 1.

Highest Common Factor of 406,630,685 using Euclid's algorithm

Highest Common Factor of 406,630,685 is 1

Step 1: Since 630 > 406, we apply the division lemma to 630 and 406, to get

630 = 406 x 1 + 224

Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 224 and 406, to get

406 = 224 x 1 + 182

Step 3: We consider the new divisor 224 and the new remainder 182, and apply the division lemma to get

224 = 182 x 1 + 42

We consider the new divisor 182 and the new remainder 42,and apply the division lemma to get

182 = 42 x 4 + 14

We consider the new divisor 42 and the new remainder 14,and apply the division lemma to get

42 = 14 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 406 and 630 is 14

Notice that 14 = HCF(42,14) = HCF(182,42) = HCF(224,182) = HCF(406,224) = HCF(630,406) .

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

Step 1: Since 685 > 14, we apply the division lemma to 685 and 14, to get

685 = 14 x 48 + 13

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 13 and 14, to get

14 = 13 x 1 + 1

Step 3: We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 685 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(685,14) .

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Frequently Asked Questions on HCF of 406, 630, 685 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 406, 630, 685?

Answer: HCF of 406, 630, 685 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 406, 630, 685 using Euclid's Algorithm?

Answer: For arbitrary numbers 406, 630, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.