Highest Common Factor of 237, 363, 262 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 237, 363, 262 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 237, 363, 262 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 237, 363, 262 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 237, 363, 262 is 1.

HCF(237, 363, 262) = 1

HCF of 237, 363, 262 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 237, 363, 262 is 1.

Highest Common Factor of 237,363,262 using Euclid's algorithm

Highest Common Factor of 237,363,262 is 1

Step 1: Since 363 > 237, we apply the division lemma to 363 and 237, to get

363 = 237 x 1 + 126

Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 126 and 237, to get

237 = 126 x 1 + 111

Step 3: We consider the new divisor 126 and the new remainder 111, and apply the division lemma to get

126 = 111 x 1 + 15

We consider the new divisor 111 and the new remainder 15,and apply the division lemma to get

111 = 15 x 7 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 237 and 363 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(111,15) = HCF(126,111) = HCF(237,126) = HCF(363,237) .

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

Step 1: Since 262 > 3, we apply the division lemma to 262 and 3, to get

262 = 3 x 87 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 262 is 1

Notice that 1 = HCF(3,1) = HCF(262,3) .

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Frequently Asked Questions on HCF of 237, 363, 262 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 237, 363, 262?

Answer: HCF of 237, 363, 262 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 237, 363, 262 using Euclid's Algorithm?

Answer: For arbitrary numbers 237, 363, 262 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.