Highest Common Factor of 997, 776, 168 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 997, 776, 168 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 997, 776, 168 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 997, 776, 168 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 997, 776, 168 is 1.

HCF(997, 776, 168) = 1

HCF of 997, 776, 168 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 997, 776, 168 is 1.

Highest Common Factor of 997,776,168 using Euclid's algorithm

Highest Common Factor of 997,776,168 is 1

Step 1: Since 997 > 776, we apply the division lemma to 997 and 776, to get

997 = 776 x 1 + 221

Step 2: Since the reminder 776 ≠ 0, we apply division lemma to 221 and 776, to get

776 = 221 x 3 + 113

Step 3: We consider the new divisor 221 and the new remainder 113, and apply the division lemma to get

221 = 113 x 1 + 108

We consider the new divisor 113 and the new remainder 108,and apply the division lemma to get

113 = 108 x 1 + 5

We consider the new divisor 108 and the new remainder 5,and apply the division lemma to get

108 = 5 x 21 + 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 997 and 776 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(108,5) = HCF(113,108) = HCF(221,113) = HCF(776,221) = HCF(997,776) .

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

Step 1: Since 168 > 1, we apply the division lemma to 168 and 1, to get

168 = 1 x 168 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 168 is 1

Notice that 1 = HCF(168,1) .

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Frequently Asked Questions on HCF of 997, 776, 168 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 997, 776, 168?

Answer: HCF of 997, 776, 168 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 997, 776, 168 using Euclid's Algorithm?

Answer: For arbitrary numbers 997, 776, 168 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.