Highest Common Factor of 262, 687, 996 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 262, 687, 996 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 262, 687, 996 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 262, 687, 996 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 262, 687, 996 is 1.

HCF(262, 687, 996) = 1

HCF of 262, 687, 996 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 262, 687, 996 is 1.

Highest Common Factor of 262,687,996 using Euclid's algorithm

Highest Common Factor of 262,687,996 is 1

Step 1: Since 687 > 262, we apply the division lemma to 687 and 262, to get

687 = 262 x 2 + 163

Step 2: Since the reminder 262 ≠ 0, we apply division lemma to 163 and 262, to get

262 = 163 x 1 + 99

Step 3: We consider the new divisor 163 and the new remainder 99, and apply the division lemma to get

163 = 99 x 1 + 64

We consider the new divisor 99 and the new remainder 64,and apply the division lemma to get

99 = 64 x 1 + 35

We consider the new divisor 64 and the new remainder 35,and apply the division lemma to get

64 = 35 x 1 + 29

We consider the new divisor 35 and the new remainder 29,and apply the division lemma to get

35 = 29 x 1 + 6

We consider the new divisor 29 and the new remainder 6,and apply the division lemma to get

29 = 6 x 4 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 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 262 and 687 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(29,6) = HCF(35,29) = HCF(64,35) = HCF(99,64) = HCF(163,99) = HCF(262,163) = HCF(687,262) .

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

Step 1: Since 996 > 1, we apply the division lemma to 996 and 1, to get

996 = 1 x 996 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 996 is 1

Notice that 1 = HCF(996,1) .

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Frequently Asked Questions on HCF of 262, 687, 996 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 262, 687, 996?

Answer: HCF of 262, 687, 996 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 262, 687, 996 using Euclid's Algorithm?

Answer: For arbitrary numbers 262, 687, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.