Highest Common Factor of 322, 560, 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 322, 560, 237 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 322, 560, 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 322, 560, 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 322, 560, 237 is 1.

HCF(322, 560, 237) = 1

HCF of 322, 560, 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 322, 560, 237 is 1.

Highest Common Factor of 322,560,237 using Euclid's algorithm

Highest Common Factor of 322,560,237 is 1

Step 1: Since 560 > 322, we apply the division lemma to 560 and 322, to get

560 = 322 x 1 + 238

Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 238 and 322, to get

322 = 238 x 1 + 84

Step 3: We consider the new divisor 238 and the new remainder 84, and apply the division lemma to get

238 = 84 x 2 + 70

We consider the new divisor 84 and the new remainder 70,and apply the division lemma to get

84 = 70 x 1 + 14

We consider the new divisor 70 and the new remainder 14,and apply the division lemma to get

70 = 14 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 322 and 560 is 14

Notice that 14 = HCF(70,14) = HCF(84,70) = HCF(238,84) = HCF(322,238) = HCF(560,322) .

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

Step 1: Since 237 > 14, we apply the division lemma to 237 and 14, to get

237 = 14 x 16 + 13

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 13 and 14, to get

14 = 13 x 1 + 1

Step 3: We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 237 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(237,14) .

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Frequently Asked Questions on HCF of 322, 560, 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 322, 560, 237?

Answer: HCF of 322, 560, 237 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 322, 560, 237 using Euclid's Algorithm?

Answer: For arbitrary numbers 322, 560, 237 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.