Highest Common Factor of 823, 465, 974 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 823, 465, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 823, 465, 974 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 823, 465, 974 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 823, 465, 974 is 1.

HCF(823, 465, 974) = 1

HCF of 823, 465, 974 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 823, 465, 974 is 1.

Highest Common Factor of 823,465,974 using Euclid's algorithm

Highest Common Factor of 823,465,974 is 1

Step 1: Since 823 > 465, we apply the division lemma to 823 and 465, to get

823 = 465 x 1 + 358

Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 358 and 465, to get

465 = 358 x 1 + 107

Step 3: We consider the new divisor 358 and the new remainder 107, and apply the division lemma to get

358 = 107 x 3 + 37

We consider the new divisor 107 and the new remainder 37,and apply the division lemma to get

107 = 37 x 2 + 33

We consider the new divisor 37 and the new remainder 33,and apply the division lemma to get

37 = 33 x 1 + 4

We consider the new divisor 33 and the new remainder 4,and apply the division lemma to get

33 = 4 x 8 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 823 and 465 is 1

Notice that 1 = HCF(4,1) = HCF(33,4) = HCF(37,33) = HCF(107,37) = HCF(358,107) = HCF(465,358) = HCF(823,465) .

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

Step 1: Since 974 > 1, we apply the division lemma to 974 and 1, to get

974 = 1 x 974 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 974 is 1

Notice that 1 = HCF(974,1) .

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Frequently Asked Questions on HCF of 823, 465, 974 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 823, 465, 974?

Answer: HCF of 823, 465, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 823, 465, 974 using Euclid's Algorithm?

Answer: For arbitrary numbers 823, 465, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.