Highest Common Factor of 898, 662, 51 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 898, 662, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 898, 662, 51 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 898, 662, 51 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 898, 662, 51 is 1.

HCF(898, 662, 51) = 1

HCF of 898, 662, 51 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 898, 662, 51 is 1.

Highest Common Factor of 898,662,51 using Euclid's algorithm

Highest Common Factor of 898,662,51 is 1

Step 1: Since 898 > 662, we apply the division lemma to 898 and 662, to get

898 = 662 x 1 + 236

Step 2: Since the reminder 662 ≠ 0, we apply division lemma to 236 and 662, to get

662 = 236 x 2 + 190

Step 3: We consider the new divisor 236 and the new remainder 190, and apply the division lemma to get

236 = 190 x 1 + 46

We consider the new divisor 190 and the new remainder 46,and apply the division lemma to get

190 = 46 x 4 + 6

We consider the new divisor 46 and the new remainder 6,and apply the division lemma to get

46 = 6 x 7 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 898 and 662 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(46,6) = HCF(190,46) = HCF(236,190) = HCF(662,236) = HCF(898,662) .

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

Step 1: Since 51 > 2, we apply the division lemma to 51 and 2, to get

51 = 2 x 25 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 51 is 1

Notice that 1 = HCF(2,1) = HCF(51,2) .

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Frequently Asked Questions on HCF of 898, 662, 51 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 898, 662, 51?

Answer: HCF of 898, 662, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 898, 662, 51 using Euclid's Algorithm?

Answer: For arbitrary numbers 898, 662, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.