# Highest Common Factor of 210, 128, 362 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 210, 128, 362 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 210, 128, 362 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 210, 128, 362 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 210, 128, 362 is 2.

HCF(210, 128, 362) = 2

## HCF of 210, 128, 362 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 210, 128, 362 is 2. ### Highest Common Factor of 210,128,362 is 2

Step 1: Since 210 > 128, we apply the division lemma to 210 and 128, to get

210 = 128 x 1 + 82

Step 2: Since the reminder 128 ≠ 0, we apply division lemma to 82 and 128, to get

128 = 82 x 1 + 46

Step 3: We consider the new divisor 82 and the new remainder 46, and apply the division lemma to get

82 = 46 x 1 + 36

We consider the new divisor 46 and the new remainder 36,and apply the division lemma to get

46 = 36 x 1 + 10

We consider the new divisor 36 and the new remainder 10,and apply the division lemma to get

36 = 10 x 3 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 210 and 128 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(36,10) = HCF(46,36) = HCF(82,46) = HCF(128,82) = HCF(210,128) .

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

Step 1: Since 362 > 2, we apply the division lemma to 362 and 2, to get

362 = 2 x 181 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 362 is 2

Notice that 2 = HCF(362,2) .

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### Frequently Asked Questions on HCF of 210, 128, 362 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 210, 128, 362?

Answer: HCF of 210, 128, 362 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 210, 128, 362 using Euclid's Algorithm?

Answer: For arbitrary numbers 210, 128, 362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.