Highest Common Factor of 591, 375, 559 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 591, 375, 559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 591, 375, 559 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 591, 375, 559 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 591, 375, 559 is 1.

HCF(591, 375, 559) = 1

HCF of 591, 375, 559 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 591, 375, 559 is 1.

Highest Common Factor of 591,375,559 using Euclid's algorithm

Highest Common Factor of 591,375,559 is 1

Step 1: Since 591 > 375, we apply the division lemma to 591 and 375, to get

591 = 375 x 1 + 216

Step 2: Since the reminder 375 ≠ 0, we apply division lemma to 216 and 375, to get

375 = 216 x 1 + 159

Step 3: We consider the new divisor 216 and the new remainder 159, and apply the division lemma to get

216 = 159 x 1 + 57

We consider the new divisor 159 and the new remainder 57,and apply the division lemma to get

159 = 57 x 2 + 45

We consider the new divisor 57 and the new remainder 45,and apply the division lemma to get

57 = 45 x 1 + 12

We consider the new divisor 45 and the new remainder 12,and apply the division lemma to get

45 = 12 x 3 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 591 and 375 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(45,12) = HCF(57,45) = HCF(159,57) = HCF(216,159) = HCF(375,216) = HCF(591,375) .

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

Step 1: Since 559 > 3, we apply the division lemma to 559 and 3, to get

559 = 3 x 186 + 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 559 is 1

Notice that 1 = HCF(3,1) = HCF(559,3) .

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Frequently Asked Questions on HCF of 591, 375, 559 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 591, 375, 559?

Answer: HCF of 591, 375, 559 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 591, 375, 559 using Euclid's Algorithm?

Answer: For arbitrary numbers 591, 375, 559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.