Highest Common Factor of 353, 585, 64 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 353, 585, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 353, 585, 64 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 353, 585, 64 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 353, 585, 64 is 1.

HCF(353, 585, 64) = 1

HCF of 353, 585, 64 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 353, 585, 64 is 1.

Highest Common Factor of 353,585,64 using Euclid's algorithm

Highest Common Factor of 353,585,64 is 1

Step 1: Since 585 > 353, we apply the division lemma to 585 and 353, to get

585 = 353 x 1 + 232

Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 232 and 353, to get

353 = 232 x 1 + 121

Step 3: We consider the new divisor 232 and the new remainder 121, and apply the division lemma to get

232 = 121 x 1 + 111

We consider the new divisor 121 and the new remainder 111,and apply the division lemma to get

121 = 111 x 1 + 10

We consider the new divisor 111 and the new remainder 10,and apply the division lemma to get

111 = 10 x 11 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 353 and 585 is 1

Notice that 1 = HCF(10,1) = HCF(111,10) = HCF(121,111) = HCF(232,121) = HCF(353,232) = HCF(585,353) .

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

Step 1: Since 64 > 1, we apply the division lemma to 64 and 1, to get

64 = 1 x 64 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64 is 1

Notice that 1 = HCF(64,1) .

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Frequently Asked Questions on HCF of 353, 585, 64 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 353, 585, 64?

Answer: HCF of 353, 585, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 353, 585, 64 using Euclid's Algorithm?

Answer: For arbitrary numbers 353, 585, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.