Highest Common Factor of 586, 952, 213, 553 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 586, 952, 213, 553 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 586, 952, 213, 553 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 586, 952, 213, 553 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 586, 952, 213, 553 is 1.

HCF(586, 952, 213, 553) = 1

HCF of 586, 952, 213, 553 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 586, 952, 213, 553 is 1.

Highest Common Factor of 586,952,213,553 using Euclid's algorithm

Highest Common Factor of 586,952,213,553 is 1

Step 1: Since 952 > 586, we apply the division lemma to 952 and 586, to get

952 = 586 x 1 + 366

Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 366 and 586, to get

586 = 366 x 1 + 220

Step 3: We consider the new divisor 366 and the new remainder 220, and apply the division lemma to get

366 = 220 x 1 + 146

We consider the new divisor 220 and the new remainder 146,and apply the division lemma to get

220 = 146 x 1 + 74

We consider the new divisor 146 and the new remainder 74,and apply the division lemma to get

146 = 74 x 1 + 72

We consider the new divisor 74 and the new remainder 72,and apply the division lemma to get

74 = 72 x 1 + 2

We consider the new divisor 72 and the new remainder 2,and apply the division lemma to get

72 = 2 x 36 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 586 and 952 is 2

Notice that 2 = HCF(72,2) = HCF(74,72) = HCF(146,74) = HCF(220,146) = HCF(366,220) = HCF(586,366) = HCF(952,586) .

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

Step 1: Since 213 > 2, we apply the division lemma to 213 and 2, to get

213 = 2 x 106 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 213 is 1

Notice that 1 = HCF(2,1) = HCF(213,2) .

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

Step 1: Since 553 > 1, we apply the division lemma to 553 and 1, to get

553 = 1 x 553 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 553 is 1

Notice that 1 = HCF(553,1) .

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Frequently Asked Questions on HCF of 586, 952, 213, 553 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 586, 952, 213, 553?

Answer: HCF of 586, 952, 213, 553 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 586, 952, 213, 553 using Euclid's Algorithm?

Answer: For arbitrary numbers 586, 952, 213, 553 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.