Highest Common Factor of 967, 684, 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 967, 684, 990 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 967, 684, 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 967, 684, 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 967, 684, 990 is 1.

HCF(967, 684, 990) = 1

HCF of 967, 684, 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 967, 684, 990 is 1.

Highest Common Factor of 967,684,990 using Euclid's algorithm

Highest Common Factor of 967,684,990 is 1

Step 1: Since 967 > 684, we apply the division lemma to 967 and 684, to get

967 = 684 x 1 + 283

Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 283 and 684, to get

684 = 283 x 2 + 118

Step 3: We consider the new divisor 283 and the new remainder 118, and apply the division lemma to get

283 = 118 x 2 + 47

We consider the new divisor 118 and the new remainder 47,and apply the division lemma to get

118 = 47 x 2 + 24

We consider the new divisor 47 and the new remainder 24,and apply the division lemma to get

47 = 24 x 1 + 23

We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get

24 = 23 x 1 + 1

We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get

23 = 1 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 967 and 684 is 1

Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(47,24) = HCF(118,47) = HCF(283,118) = HCF(684,283) = HCF(967,684) .

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

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

990 = 1 x 990 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 990 is 1

Notice that 1 = HCF(990,1) .

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Frequently Asked Questions on HCF of 967, 684, 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 967, 684, 990?

Answer: HCF of 967, 684, 990 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 967, 684, 990 using Euclid's Algorithm?

Answer: For arbitrary numbers 967, 684, 990 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.