Highest Common Factor of 896, 658, 65 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 896, 658, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 896, 658, 65 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 896, 658, 65 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 896, 658, 65 is 1.

HCF(896, 658, 65) = 1

HCF of 896, 658, 65 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 896, 658, 65 is 1.

Highest Common Factor of 896,658,65 using Euclid's algorithm

Highest Common Factor of 896,658,65 is 1

Step 1: Since 896 > 658, we apply the division lemma to 896 and 658, to get

896 = 658 x 1 + 238

Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 238 and 658, to get

658 = 238 x 2 + 182

Step 3: We consider the new divisor 238 and the new remainder 182, and apply the division lemma to get

238 = 182 x 1 + 56

We consider the new divisor 182 and the new remainder 56,and apply the division lemma to get

182 = 56 x 3 + 14

We consider the new divisor 56 and the new remainder 14,and apply the division lemma to get

56 = 14 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 896 and 658 is 14

Notice that 14 = HCF(56,14) = HCF(182,56) = HCF(238,182) = HCF(658,238) = HCF(896,658) .

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

Step 1: Since 65 > 14, we apply the division lemma to 65 and 14, to get

65 = 14 x 4 + 9

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 9 and 14, to get

14 = 9 x 1 + 5

Step 3: We consider the new divisor 9 and the new remainder 5, and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 65 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(65,14) .

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Frequently Asked Questions on HCF of 896, 658, 65 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 896, 658, 65?

Answer: HCF of 896, 658, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 896, 658, 65 using Euclid's Algorithm?

Answer: For arbitrary numbers 896, 658, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.