Highest Common Factor of 742, 686, 709 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 742, 686, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 742, 686, 709 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 742, 686, 709 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 742, 686, 709 is 1.

HCF(742, 686, 709) = 1

HCF of 742, 686, 709 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 742, 686, 709 is 1.

Highest Common Factor of 742,686,709 using Euclid's algorithm

Highest Common Factor of 742,686,709 is 1

Step 1: Since 742 > 686, we apply the division lemma to 742 and 686, to get

742 = 686 x 1 + 56

Step 2: Since the reminder 686 ≠ 0, we apply division lemma to 56 and 686, to get

686 = 56 x 12 + 14

Step 3: We consider the new divisor 56 and the new remainder 14, and apply the division lemma to get

56 = 14 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 742 and 686 is 14

Notice that 14 = HCF(56,14) = HCF(686,56) = HCF(742,686) .

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

Step 1: Since 709 > 14, we apply the division lemma to 709 and 14, to get

709 = 14 x 50 + 9

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 9 and 14, to get

14 = 9 x 1 + 5

Step 3: We consider the new divisor 9 and the new remainder 5, and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

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 14 and 709 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(709,14) .

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Frequently Asked Questions on HCF of 742, 686, 709 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 742, 686, 709?

Answer: HCF of 742, 686, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 742, 686, 709 using Euclid's Algorithm?

Answer: For arbitrary numbers 742, 686, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.