Highest Common Factor of 223, 808, 706 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 223, 808, 706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 223, 808, 706 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 223, 808, 706 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 223, 808, 706 is 1.

HCF(223, 808, 706) = 1

HCF of 223, 808, 706 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 223, 808, 706 is 1.

Highest Common Factor of 223,808,706 using Euclid's algorithm

Highest Common Factor of 223,808,706 is 1

Step 1: Since 808 > 223, we apply the division lemma to 808 and 223, to get

808 = 223 x 3 + 139

Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 139 and 223, to get

223 = 139 x 1 + 84

Step 3: We consider the new divisor 139 and the new remainder 84, and apply the division lemma to get

139 = 84 x 1 + 55

We consider the new divisor 84 and the new remainder 55,and apply the division lemma to get

84 = 55 x 1 + 29

We consider the new divisor 55 and the new remainder 29,and apply the division lemma to get

55 = 29 x 1 + 26

We consider the new divisor 29 and the new remainder 26,and apply the division lemma to get

29 = 26 x 1 + 3

We consider the new divisor 26 and the new remainder 3,and apply the division lemma to get

26 = 3 x 8 + 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 223 and 808 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(29,26) = HCF(55,29) = HCF(84,55) = HCF(139,84) = HCF(223,139) = HCF(808,223) .

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

Step 1: Since 706 > 1, we apply the division lemma to 706 and 1, to get

706 = 1 x 706 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 706 is 1

Notice that 1 = HCF(706,1) .

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Frequently Asked Questions on HCF of 223, 808, 706 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 223, 808, 706?

Answer: HCF of 223, 808, 706 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 223, 808, 706 using Euclid's Algorithm?

Answer: For arbitrary numbers 223, 808, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.