Highest Common Factor of 359, 585, 735 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 359, 585, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 359, 585, 735 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 359, 585, 735 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 359, 585, 735 is 1.

HCF(359, 585, 735) = 1

HCF of 359, 585, 735 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 359, 585, 735 is 1.

Highest Common Factor of 359,585,735 using Euclid's algorithm

Highest Common Factor of 359,585,735 is 1

Step 1: Since 585 > 359, we apply the division lemma to 585 and 359, to get

585 = 359 x 1 + 226

Step 2: Since the reminder 359 ≠ 0, we apply division lemma to 226 and 359, to get

359 = 226 x 1 + 133

Step 3: We consider the new divisor 226 and the new remainder 133, and apply the division lemma to get

226 = 133 x 1 + 93

We consider the new divisor 133 and the new remainder 93,and apply the division lemma to get

133 = 93 x 1 + 40

We consider the new divisor 93 and the new remainder 40,and apply the division lemma to get

93 = 40 x 2 + 13

We consider the new divisor 40 and the new remainder 13,and apply the division lemma to get

40 = 13 x 3 + 1

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 359 and 585 is 1

Notice that 1 = HCF(13,1) = HCF(40,13) = HCF(93,40) = HCF(133,93) = HCF(226,133) = HCF(359,226) = HCF(585,359) .

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

Step 1: Since 735 > 1, we apply the division lemma to 735 and 1, to get

735 = 1 x 735 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 735 is 1

Notice that 1 = HCF(735,1) .

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Frequently Asked Questions on HCF of 359, 585, 735 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 359, 585, 735?

Answer: HCF of 359, 585, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 359, 585, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 359, 585, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.