Highest Common Factor of 446, 742, 691 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 446, 742, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 446, 742, 691 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 446, 742, 691 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 446, 742, 691 is 1.

HCF(446, 742, 691) = 1

HCF of 446, 742, 691 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 446, 742, 691 is 1.

Highest Common Factor of 446,742,691 using Euclid's algorithm

Highest Common Factor of 446,742,691 is 1

Step 1: Since 742 > 446, we apply the division lemma to 742 and 446, to get

742 = 446 x 1 + 296

Step 2: Since the reminder 446 ≠ 0, we apply division lemma to 296 and 446, to get

446 = 296 x 1 + 150

Step 3: We consider the new divisor 296 and the new remainder 150, and apply the division lemma to get

296 = 150 x 1 + 146

We consider the new divisor 150 and the new remainder 146,and apply the division lemma to get

150 = 146 x 1 + 4

We consider the new divisor 146 and the new remainder 4,and apply the division lemma to get

146 = 4 x 36 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 446 and 742 is 2

Notice that 2 = HCF(4,2) = HCF(146,4) = HCF(150,146) = HCF(296,150) = HCF(446,296) = HCF(742,446) .

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

Step 1: Since 691 > 2, we apply the division lemma to 691 and 2, to get

691 = 2 x 345 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 691 is 1

Notice that 1 = HCF(2,1) = HCF(691,2) .

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Frequently Asked Questions on HCF of 446, 742, 691 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 446, 742, 691?

Answer: HCF of 446, 742, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 446, 742, 691 using Euclid's Algorithm?

Answer: For arbitrary numbers 446, 742, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.