Highest Common Factor of 208, 702, 888 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 208, 702, 888 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 208, 702, 888 is 2 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 208, 702, 888 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 208, 702, 888 is 2.

HCF(208, 702, 888) = 2

HCF of 208, 702, 888 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 208, 702, 888 is 2.

Highest Common Factor of 208,702,888 using Euclid's algorithm

Highest Common Factor of 208,702,888 is 2

Step 1: Since 702 > 208, we apply the division lemma to 702 and 208, to get

702 = 208 x 3 + 78

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 78 and 208, to get

208 = 78 x 2 + 52

Step 3: We consider the new divisor 78 and the new remainder 52, and apply the division lemma to get

78 = 52 x 1 + 26

We consider the new divisor 52 and the new remainder 26, and apply the division lemma to get

52 = 26 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 208 and 702 is 26

Notice that 26 = HCF(52,26) = HCF(78,52) = HCF(208,78) = HCF(702,208) .

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

Step 1: Since 888 > 26, we apply the division lemma to 888 and 26, to get

888 = 26 x 34 + 4

Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 4 and 26, to get

26 = 4 x 6 + 2

Step 3: 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 26 and 888 is 2

Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(888,26) .

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Frequently Asked Questions on HCF of 208, 702, 888 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 208, 702, 888?

Answer: HCF of 208, 702, 888 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 208, 702, 888 using Euclid's Algorithm?

Answer: For arbitrary numbers 208, 702, 888 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.