Highest Common Factor of 461, 833, 678 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 461, 833, 678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 461, 833, 678 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 461, 833, 678 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 461, 833, 678 is 1.

HCF(461, 833, 678) = 1

HCF of 461, 833, 678 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 461, 833, 678 is 1.

Highest Common Factor of 461,833,678 using Euclid's algorithm

Highest Common Factor of 461,833,678 is 1

Step 1: Since 833 > 461, we apply the division lemma to 833 and 461, to get

833 = 461 x 1 + 372

Step 2: Since the reminder 461 ≠ 0, we apply division lemma to 372 and 461, to get

461 = 372 x 1 + 89

Step 3: We consider the new divisor 372 and the new remainder 89, and apply the division lemma to get

372 = 89 x 4 + 16

We consider the new divisor 89 and the new remainder 16,and apply the division lemma to get

89 = 16 x 5 + 9

We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get

16 = 9 x 1 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 461 and 833 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(89,16) = HCF(372,89) = HCF(461,372) = HCF(833,461) .

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

Step 1: Since 678 > 1, we apply the division lemma to 678 and 1, to get

678 = 1 x 678 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 678 is 1

Notice that 1 = HCF(678,1) .

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Frequently Asked Questions on HCF of 461, 833, 678 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 461, 833, 678?

Answer: HCF of 461, 833, 678 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 461, 833, 678 using Euclid's Algorithm?

Answer: For arbitrary numbers 461, 833, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.