Highest Common Factor of 698, 882, 592 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, 882, 592 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 698, 882, 592 is 2 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, 882, 592 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, 882, 592 is 2.

HCF(698, 882, 592) = 2

HCF of 698, 882, 592 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, 882, 592 is 2.

Highest Common Factor of 698,882,592 using Euclid's algorithm

Highest Common Factor of 698,882,592 is 2

Step 1: Since 882 > 698, we apply the division lemma to 882 and 698, to get

882 = 698 x 1 + 184

Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 184 and 698, to get

698 = 184 x 3 + 146

Step 3: We consider the new divisor 184 and the new remainder 146, and apply the division lemma to get

184 = 146 x 1 + 38

We consider the new divisor 146 and the new remainder 38,and apply the division lemma to get

146 = 38 x 3 + 32

We consider the new divisor 38 and the new remainder 32,and apply the division lemma to get

38 = 32 x 1 + 6

We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get

32 = 6 x 5 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 698 and 882 is 2

Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(146,38) = HCF(184,146) = HCF(698,184) = HCF(882,698) .

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

Step 1: Since 592 > 2, we apply the division lemma to 592 and 2, to get

592 = 2 x 296 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 592 is 2

Notice that 2 = HCF(592,2) .

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Frequently Asked Questions on HCF of 698, 882, 592 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, 882, 592?

Answer: HCF of 698, 882, 592 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 698, 882, 592 using Euclid's Algorithm?

Answer: For arbitrary numbers 698, 882, 592 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.