Highest Common Factor of 698, 66 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 698, 66 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 698, 66 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 698, 66 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 698, 66 is 2.

HCF(698, 66) = 2

HCF of 698, 66 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 698, 66 is 2.

Highest Common Factor of 698,66 using Euclid's algorithm

Highest Common Factor of 698,66 is 2

Step 1: Since 698 > 66, we apply the division lemma to 698 and 66, to get

698 = 66 x 10 + 38

Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 38 and 66, to get

66 = 38 x 1 + 28

Step 3: We consider the new divisor 38 and the new remainder 28, and apply the division lemma to get

38 = 28 x 1 + 10

We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get

28 = 10 x 2 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 698 and 66 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(66,38) = HCF(698,66) .

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Frequently Asked Questions on HCF of 698, 66 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 698, 66?

Answer: HCF of 698, 66 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 698, 66 using Euclid's Algorithm?

Answer: For arbitrary numbers 698, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.