Highest Common Factor of 722, 7083 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 722, 7083 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 722, 7083 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 722, 7083 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 722, 7083 is 1.

HCF(722, 7083) = 1

HCF of 722, 7083 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 722, 7083 is 1.

Highest Common Factor of 722,7083 using Euclid's algorithm

Highest Common Factor of 722,7083 is 1

Step 1: Since 7083 > 722, we apply the division lemma to 7083 and 722, to get

7083 = 722 x 9 + 585

Step 2: Since the reminder 722 ≠ 0, we apply division lemma to 585 and 722, to get

722 = 585 x 1 + 137

Step 3: We consider the new divisor 585 and the new remainder 137, and apply the division lemma to get

585 = 137 x 4 + 37

We consider the new divisor 137 and the new remainder 37,and apply the division lemma to get

137 = 37 x 3 + 26

We consider the new divisor 37 and the new remainder 26,and apply the division lemma to get

37 = 26 x 1 + 11

We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get

26 = 11 x 2 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

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

4 = 3 x 1 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 722 and 7083 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(37,26) = HCF(137,37) = HCF(585,137) = HCF(722,585) = HCF(7083,722) .

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Frequently Asked Questions on HCF of 722, 7083 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 722, 7083?

Answer: HCF of 722, 7083 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 722, 7083 using Euclid's Algorithm?

Answer: For arbitrary numbers 722, 7083 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.