Highest Common Factor of 723, 165, 640 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 723, 165, 640 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 723, 165, 640 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 723, 165, 640 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 723, 165, 640 is 1.

HCF(723, 165, 640) = 1

HCF of 723, 165, 640 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 723, 165, 640 is 1.

Highest Common Factor of 723,165,640 using Euclid's algorithm

Highest Common Factor of 723,165,640 is 1

Step 1: Since 723 > 165, we apply the division lemma to 723 and 165, to get

723 = 165 x 4 + 63

Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 63 and 165, to get

165 = 63 x 2 + 39

Step 3: We consider the new divisor 63 and the new remainder 39, and apply the division lemma to get

63 = 39 x 1 + 24

We consider the new divisor 39 and the new remainder 24,and apply the division lemma to get

39 = 24 x 1 + 15

We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 723 and 165 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(63,39) = HCF(165,63) = HCF(723,165) .

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

Step 1: Since 640 > 3, we apply the division lemma to 640 and 3, to get

640 = 3 x 213 + 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 640 is 1

Notice that 1 = HCF(3,1) = HCF(640,3) .

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Frequently Asked Questions on HCF of 723, 165, 640 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 723, 165, 640?

Answer: HCF of 723, 165, 640 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 723, 165, 640 using Euclid's Algorithm?

Answer: For arbitrary numbers 723, 165, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.