Highest Common Factor of 687, 923, 46 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 687, 923, 46 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 687, 923, 46 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 687, 923, 46 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 687, 923, 46 is 1.

HCF(687, 923, 46) = 1

HCF of 687, 923, 46 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 687, 923, 46 is 1.

Highest Common Factor of 687,923,46 using Euclid's algorithm

Highest Common Factor of 687,923,46 is 1

Step 1: Since 923 > 687, we apply the division lemma to 923 and 687, to get

923 = 687 x 1 + 236

Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 236 and 687, to get

687 = 236 x 2 + 215

Step 3: We consider the new divisor 236 and the new remainder 215, and apply the division lemma to get

236 = 215 x 1 + 21

We consider the new divisor 215 and the new remainder 21,and apply the division lemma to get

215 = 21 x 10 + 5

We consider the new divisor 21 and the new remainder 5,and apply the division lemma to get

21 = 5 x 4 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 687 and 923 is 1

Notice that 1 = HCF(5,1) = HCF(21,5) = HCF(215,21) = HCF(236,215) = HCF(687,236) = HCF(923,687) .

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

Step 1: Since 46 > 1, we apply the division lemma to 46 and 1, to get

46 = 1 x 46 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 46 is 1

Notice that 1 = HCF(46,1) .

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Frequently Asked Questions on HCF of 687, 923, 46 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 687, 923, 46?

Answer: HCF of 687, 923, 46 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 687, 923, 46 using Euclid's Algorithm?

Answer: For arbitrary numbers 687, 923, 46 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.