Highest Common Factor of 698, 827, 493 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 698, 827, 493 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 698, 827, 493 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 698, 827, 493 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 698, 827, 493 is 1.

HCF(698, 827, 493) = 1

HCF of 698, 827, 493 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 698, 827, 493 is 1.

Highest Common Factor of 698,827,493 using Euclid's algorithm

Highest Common Factor of 698,827,493 is 1

Step 1: Since 827 > 698, we apply the division lemma to 827 and 698, to get

827 = 698 x 1 + 129

Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 129 and 698, to get

698 = 129 x 5 + 53

Step 3: We consider the new divisor 129 and the new remainder 53, and apply the division lemma to get

129 = 53 x 2 + 23

We consider the new divisor 53 and the new remainder 23,and apply the division lemma to get

53 = 23 x 2 + 7

We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get

23 = 7 x 3 + 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 698 and 827 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(53,23) = HCF(129,53) = HCF(698,129) = HCF(827,698) .

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

Step 1: Since 493 > 1, we apply the division lemma to 493 and 1, to get

493 = 1 x 493 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 493 is 1

Notice that 1 = HCF(493,1) .

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Frequently Asked Questions on HCF of 698, 827, 493 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 698, 827, 493?

Answer: HCF of 698, 827, 493 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 698, 827, 493 using Euclid's Algorithm?

Answer: For arbitrary numbers 698, 827, 493 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.