Highest Common Factor of 967, 1667, 3649 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 967, 1667, 3649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 967, 1667, 3649 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 967, 1667, 3649 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 967, 1667, 3649 is 1.

HCF(967, 1667, 3649) = 1

HCF of 967, 1667, 3649 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 967, 1667, 3649 is 1.

Highest Common Factor of 967,1667,3649 using Euclid's algorithm

Highest Common Factor of 967,1667,3649 is 1

Step 1: Since 1667 > 967, we apply the division lemma to 1667 and 967, to get

1667 = 967 x 1 + 700

Step 2: Since the reminder 967 ≠ 0, we apply division lemma to 700 and 967, to get

967 = 700 x 1 + 267

Step 3: We consider the new divisor 700 and the new remainder 267, and apply the division lemma to get

700 = 267 x 2 + 166

We consider the new divisor 267 and the new remainder 166,and apply the division lemma to get

267 = 166 x 1 + 101

We consider the new divisor 166 and the new remainder 101,and apply the division lemma to get

166 = 101 x 1 + 65

We consider the new divisor 101 and the new remainder 65,and apply the division lemma to get

101 = 65 x 1 + 36

We consider the new divisor 65 and the new remainder 36,and apply the division lemma to get

65 = 36 x 1 + 29

We consider the new divisor 36 and the new remainder 29,and apply the division lemma to get

36 = 29 x 1 + 7

We consider the new divisor 29 and the new remainder 7,and apply the division lemma to get

29 = 7 x 4 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 967 and 1667 is 1

Notice that 1 = HCF(7,1) = HCF(29,7) = HCF(36,29) = HCF(65,36) = HCF(101,65) = HCF(166,101) = HCF(267,166) = HCF(700,267) = HCF(967,700) = HCF(1667,967) .

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

Step 1: Since 3649 > 1, we apply the division lemma to 3649 and 1, to get

3649 = 1 x 3649 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3649 is 1

Notice that 1 = HCF(3649,1) .

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Frequently Asked Questions on HCF of 967, 1667, 3649 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 967, 1667, 3649?

Answer: HCF of 967, 1667, 3649 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 967, 1667, 3649 using Euclid's Algorithm?

Answer: For arbitrary numbers 967, 1667, 3649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.