Highest Common Factor of 991, 818, 354 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, 818, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 991, 818, 354 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, 818, 354 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, 818, 354 is 1.

HCF(991, 818, 354) = 1

HCF of 991, 818, 354 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, 818, 354 is 1.

Highest Common Factor of 991,818,354 using Euclid's algorithm

Highest Common Factor of 991,818,354 is 1

Step 1: Since 991 > 818, we apply the division lemma to 991 and 818, to get

991 = 818 x 1 + 173

Step 2: Since the reminder 818 ≠ 0, we apply division lemma to 173 and 818, to get

818 = 173 x 4 + 126

Step 3: We consider the new divisor 173 and the new remainder 126, and apply the division lemma to get

173 = 126 x 1 + 47

We consider the new divisor 126 and the new remainder 47,and apply the division lemma to get

126 = 47 x 2 + 32

We consider the new divisor 47 and the new remainder 32,and apply the division lemma to get

47 = 32 x 1 + 15

We consider the new divisor 32 and the new remainder 15,and apply the division lemma to get

32 = 15 x 2 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 991 and 818 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(32,15) = HCF(47,32) = HCF(126,47) = HCF(173,126) = HCF(818,173) = HCF(991,818) .

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

Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get

354 = 1 x 354 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1

Notice that 1 = HCF(354,1) .

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Frequently Asked Questions on HCF of 991, 818, 354 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, 818, 354?

Answer: HCF of 991, 818, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 991, 818, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 991, 818, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.