Highest Common Factor of 669, 5708, 9167 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 669, 5708, 9167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 669, 5708, 9167 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 669, 5708, 9167 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 669, 5708, 9167 is 1.

HCF(669, 5708, 9167) = 1

HCF of 669, 5708, 9167 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 669, 5708, 9167 is 1.

Highest Common Factor of 669,5708,9167 using Euclid's algorithm

Highest Common Factor of 669,5708,9167 is 1

Step 1: Since 5708 > 669, we apply the division lemma to 5708 and 669, to get

5708 = 669 x 8 + 356

Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 356 and 669, to get

669 = 356 x 1 + 313

Step 3: We consider the new divisor 356 and the new remainder 313, and apply the division lemma to get

356 = 313 x 1 + 43

We consider the new divisor 313 and the new remainder 43,and apply the division lemma to get

313 = 43 x 7 + 12

We consider the new divisor 43 and the new remainder 12,and apply the division lemma to get

43 = 12 x 3 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 669 and 5708 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(313,43) = HCF(356,313) = HCF(669,356) = HCF(5708,669) .

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

Step 1: Since 9167 > 1, we apply the division lemma to 9167 and 1, to get

9167 = 1 x 9167 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9167 is 1

Notice that 1 = HCF(9167,1) .

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Frequently Asked Questions on HCF of 669, 5708, 9167 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 669, 5708, 9167?

Answer: HCF of 669, 5708, 9167 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 669, 5708, 9167 using Euclid's Algorithm?

Answer: For arbitrary numbers 669, 5708, 9167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.