Highest Common Factor of 352, 555, 588 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 352, 555, 588 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 352, 555, 588 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 352, 555, 588 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 352, 555, 588 is 1.

HCF(352, 555, 588) = 1

HCF of 352, 555, 588 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 352, 555, 588 is 1.

Highest Common Factor of 352,555,588 using Euclid's algorithm

Highest Common Factor of 352,555,588 is 1

Step 1: Since 555 > 352, we apply the division lemma to 555 and 352, to get

555 = 352 x 1 + 203

Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 203 and 352, to get

352 = 203 x 1 + 149

Step 3: We consider the new divisor 203 and the new remainder 149, and apply the division lemma to get

203 = 149 x 1 + 54

We consider the new divisor 149 and the new remainder 54,and apply the division lemma to get

149 = 54 x 2 + 41

We consider the new divisor 54 and the new remainder 41,and apply the division lemma to get

54 = 41 x 1 + 13

We consider the new divisor 41 and the new remainder 13,and apply the division lemma to get

41 = 13 x 3 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 352 and 555 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(41,13) = HCF(54,41) = HCF(149,54) = HCF(203,149) = HCF(352,203) = HCF(555,352) .

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

Step 1: Since 588 > 1, we apply the division lemma to 588 and 1, to get

588 = 1 x 588 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 588 is 1

Notice that 1 = HCF(588,1) .

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Frequently Asked Questions on HCF of 352, 555, 588 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 352, 555, 588?

Answer: HCF of 352, 555, 588 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 352, 555, 588 using Euclid's Algorithm?

Answer: For arbitrary numbers 352, 555, 588 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.