Highest Common Factor of 7636, 208 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 7636, 208 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 7636, 208 is 4 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 7636, 208 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 7636, 208 is 4.

HCF(7636, 208) = 4

HCF of 7636, 208 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 7636, 208 is 4.

Highest Common Factor of 7636,208 using Euclid's algorithm

Highest Common Factor of 7636,208 is 4

Step 1: Since 7636 > 208, we apply the division lemma to 7636 and 208, to get

7636 = 208 x 36 + 148

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 148 and 208, to get

208 = 148 x 1 + 60

Step 3: We consider the new divisor 148 and the new remainder 60, and apply the division lemma to get

148 = 60 x 2 + 28

We consider the new divisor 60 and the new remainder 28,and apply the division lemma to get

60 = 28 x 2 + 4

We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get

28 = 4 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 7636 and 208 is 4

Notice that 4 = HCF(28,4) = HCF(60,28) = HCF(148,60) = HCF(208,148) = HCF(7636,208) .

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Frequently Asked Questions on HCF of 7636, 208 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 7636, 208?

Answer: HCF of 7636, 208 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7636, 208 using Euclid's Algorithm?

Answer: For arbitrary numbers 7636, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.