Highest Common Factor of 210, 372, 169 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, 372, 169 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 210, 372, 169 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 210, 372, 169 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, 372, 169 is 1.

HCF(210, 372, 169) = 1

HCF of 210, 372, 169 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 210, 372, 169 is 1.

Highest Common Factor of 210,372,169 using Euclid's algorithm

Highest Common Factor of 210,372,169 is 1

Step 1: Since 372 > 210, we apply the division lemma to 372 and 210, to get

372 = 210 x 1 + 162

Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 162 and 210, to get

210 = 162 x 1 + 48

Step 3: We consider the new divisor 162 and the new remainder 48, and apply the division lemma to get

162 = 48 x 3 + 18

We consider the new divisor 48 and the new remainder 18,and apply the division lemma to get

48 = 18 x 2 + 12

We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get

18 = 12 x 1 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 210 and 372 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(48,18) = HCF(162,48) = HCF(210,162) = HCF(372,210) .

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

Step 1: Since 169 > 6, we apply the division lemma to 169 and 6, to get

169 = 6 x 28 + 1

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 169 is 1

Notice that 1 = HCF(6,1) = HCF(169,6) .

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Frequently Asked Questions on HCF of 210, 372, 169 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, 372, 169?

Answer: HCF of 210, 372, 169 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 210, 372, 169 using Euclid's Algorithm?

Answer: For arbitrary numbers 210, 372, 169 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.