Highest Common Factor of 874, 511, 406 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 874, 511, 406 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 874, 511, 406 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 874, 511, 406 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 874, 511, 406 is 1.

HCF(874, 511, 406) = 1

HCF of 874, 511, 406 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 874, 511, 406 is 1.

Highest Common Factor of 874,511,406 using Euclid's algorithm

Highest Common Factor of 874,511,406 is 1

Step 1: Since 874 > 511, we apply the division lemma to 874 and 511, to get

874 = 511 x 1 + 363

Step 2: Since the reminder 511 ≠ 0, we apply division lemma to 363 and 511, to get

511 = 363 x 1 + 148

Step 3: We consider the new divisor 363 and the new remainder 148, and apply the division lemma to get

363 = 148 x 2 + 67

We consider the new divisor 148 and the new remainder 67,and apply the division lemma to get

148 = 67 x 2 + 14

We consider the new divisor 67 and the new remainder 14,and apply the division lemma to get

67 = 14 x 4 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 874 and 511 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(67,14) = HCF(148,67) = HCF(363,148) = HCF(511,363) = HCF(874,511) .

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

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

406 = 1 x 406 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 406 is 1

Notice that 1 = HCF(406,1) .

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Frequently Asked Questions on HCF of 874, 511, 406 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 874, 511, 406?

Answer: HCF of 874, 511, 406 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 874, 511, 406 using Euclid's Algorithm?

Answer: For arbitrary numbers 874, 511, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.