Highest Common Factor of 667, 990 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 667, 990 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 667, 990 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 667, 990 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 667, 990 is 1.

HCF(667, 990) = 1

HCF of 667, 990 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 667, 990 is 1.

Highest Common Factor of 667,990 using Euclid's algorithm

Highest Common Factor of 667,990 is 1

Step 1: Since 990 > 667, we apply the division lemma to 990 and 667, to get

990 = 667 x 1 + 323

Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 323 and 667, to get

667 = 323 x 2 + 21

Step 3: We consider the new divisor 323 and the new remainder 21, and apply the division lemma to get

323 = 21 x 15 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 667 and 990 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(323,21) = HCF(667,323) = HCF(990,667) .

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Frequently Asked Questions on HCF of 667, 990 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 667, 990?

Answer: HCF of 667, 990 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 667, 990 using Euclid's Algorithm?

Answer: For arbitrary numbers 667, 990 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.