Highest Common Factor of 732, 405, 85 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 732, 405, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 732, 405, 85 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 732, 405, 85 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 732, 405, 85 is 1.

HCF(732, 405, 85) = 1

HCF of 732, 405, 85 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 732, 405, 85 is 1.

Highest Common Factor of 732,405,85 using Euclid's algorithm

Highest Common Factor of 732,405,85 is 1

Step 1: Since 732 > 405, we apply the division lemma to 732 and 405, to get

732 = 405 x 1 + 327

Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 327 and 405, to get

405 = 327 x 1 + 78

Step 3: We consider the new divisor 327 and the new remainder 78, and apply the division lemma to get

327 = 78 x 4 + 15

We consider the new divisor 78 and the new remainder 15,and apply the division lemma to get

78 = 15 x 5 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 732 and 405 is 3

Notice that 3 = HCF(15,3) = HCF(78,15) = HCF(327,78) = HCF(405,327) = HCF(732,405) .

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

Step 1: Since 85 > 3, we apply the division lemma to 85 and 3, to get

85 = 3 x 28 + 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 85 is 1

Notice that 1 = HCF(3,1) = HCF(85,3) .

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Frequently Asked Questions on HCF of 732, 405, 85 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 732, 405, 85?

Answer: HCF of 732, 405, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 732, 405, 85 using Euclid's Algorithm?

Answer: For arbitrary numbers 732, 405, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.