Highest Common Factor of 632, 698, 880 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 632, 698, 880 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 632, 698, 880 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 632, 698, 880 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 632, 698, 880 is 2.

HCF(632, 698, 880) = 2

HCF of 632, 698, 880 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 632, 698, 880 is 2.

Highest Common Factor of 632,698,880 using Euclid's algorithm

Highest Common Factor of 632,698,880 is 2

Step 1: Since 698 > 632, we apply the division lemma to 698 and 632, to get

698 = 632 x 1 + 66

Step 2: Since the reminder 632 ≠ 0, we apply division lemma to 66 and 632, to get

632 = 66 x 9 + 38

Step 3: We consider the new divisor 66 and the new remainder 38, and apply the division lemma to get

66 = 38 x 1 + 28

We consider the new divisor 38 and the new remainder 28,and apply the division lemma to get

38 = 28 x 1 + 10

We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get

28 = 10 x 2 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 632 and 698 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(66,38) = HCF(632,66) = HCF(698,632) .

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

Step 1: Since 880 > 2, we apply the division lemma to 880 and 2, to get

880 = 2 x 440 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 880 is 2

Notice that 2 = HCF(880,2) .

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Frequently Asked Questions on HCF of 632, 698, 880 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 632, 698, 880?

Answer: HCF of 632, 698, 880 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 632, 698, 880 using Euclid's Algorithm?

Answer: For arbitrary numbers 632, 698, 880 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.