Highest Common Factor of 607, 213, 237 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 607, 213, 237 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 607, 213, 237 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 607, 213, 237 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 607, 213, 237 is 1.

HCF(607, 213, 237) = 1

HCF of 607, 213, 237 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 607, 213, 237 is 1.

Highest Common Factor of 607,213,237 using Euclid's algorithm

Highest Common Factor of 607,213,237 is 1

Step 1: Since 607 > 213, we apply the division lemma to 607 and 213, to get

607 = 213 x 2 + 181

Step 2: Since the reminder 213 ≠ 0, we apply division lemma to 181 and 213, to get

213 = 181 x 1 + 32

Step 3: We consider the new divisor 181 and the new remainder 32, and apply the division lemma to get

181 = 32 x 5 + 21

We consider the new divisor 32 and the new remainder 21,and apply the division lemma to get

32 = 21 x 1 + 11

We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get

21 = 11 x 1 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 607 and 213 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) = HCF(181,32) = HCF(213,181) = HCF(607,213) .

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

Step 1: Since 237 > 1, we apply the division lemma to 237 and 1, to get

237 = 1 x 237 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 237 is 1

Notice that 1 = HCF(237,1) .

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Frequently Asked Questions on HCF of 607, 213, 237 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 607, 213, 237?

Answer: HCF of 607, 213, 237 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 607, 213, 237 using Euclid's Algorithm?

Answer: For arbitrary numbers 607, 213, 237 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.