Highest Common Factor of 813, 988, 160 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 813, 988, 160 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 813, 988, 160 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 813, 988, 160 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 813, 988, 160 is 1.

HCF(813, 988, 160) = 1

HCF of 813, 988, 160 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 813, 988, 160 is 1.

Highest Common Factor of 813,988,160 using Euclid's algorithm

Highest Common Factor of 813,988,160 is 1

Step 1: Since 988 > 813, we apply the division lemma to 988 and 813, to get

988 = 813 x 1 + 175

Step 2: Since the reminder 813 ≠ 0, we apply division lemma to 175 and 813, to get

813 = 175 x 4 + 113

Step 3: We consider the new divisor 175 and the new remainder 113, and apply the division lemma to get

175 = 113 x 1 + 62

We consider the new divisor 113 and the new remainder 62,and apply the division lemma to get

113 = 62 x 1 + 51

We consider the new divisor 62 and the new remainder 51,and apply the division lemma to get

62 = 51 x 1 + 11

We consider the new divisor 51 and the new remainder 11,and apply the division lemma to get

51 = 11 x 4 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 813 and 988 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(51,11) = HCF(62,51) = HCF(113,62) = HCF(175,113) = HCF(813,175) = HCF(988,813) .

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

Step 1: Since 160 > 1, we apply the division lemma to 160 and 1, to get

160 = 1 x 160 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 160 is 1

Notice that 1 = HCF(160,1) .

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Frequently Asked Questions on HCF of 813, 988, 160 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 813, 988, 160?

Answer: HCF of 813, 988, 160 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 813, 988, 160 using Euclid's Algorithm?

Answer: For arbitrary numbers 813, 988, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.