Highest Common Factor of 991, 622, 81 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 991, 622, 81 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 991, 622, 81 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 991, 622, 81 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 991, 622, 81 is 1.

HCF(991, 622, 81) = 1

HCF of 991, 622, 81 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 991, 622, 81 is 1.

Highest Common Factor of 991,622,81 using Euclid's algorithm

Highest Common Factor of 991,622,81 is 1

Step 1: Since 991 > 622, we apply the division lemma to 991 and 622, to get

991 = 622 x 1 + 369

Step 2: Since the reminder 622 ≠ 0, we apply division lemma to 369 and 622, to get

622 = 369 x 1 + 253

Step 3: We consider the new divisor 369 and the new remainder 253, and apply the division lemma to get

369 = 253 x 1 + 116

We consider the new divisor 253 and the new remainder 116,and apply the division lemma to get

253 = 116 x 2 + 21

We consider the new divisor 116 and the new remainder 21,and apply the division lemma to get

116 = 21 x 5 + 11

We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get

21 = 11 x 1 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 991 and 622 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(116,21) = HCF(253,116) = HCF(369,253) = HCF(622,369) = HCF(991,622) .

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

Step 1: Since 81 > 1, we apply the division lemma to 81 and 1, to get

81 = 1 x 81 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 81 is 1

Notice that 1 = HCF(81,1) .

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Frequently Asked Questions on HCF of 991, 622, 81 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 991, 622, 81?

Answer: HCF of 991, 622, 81 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 991, 622, 81 using Euclid's Algorithm?

Answer: For arbitrary numbers 991, 622, 81 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.