Highest Common Factor of 585, 748, 639, 729 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 585, 748, 639, 729 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 748, 639, 729 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 585, 748, 639, 729 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 585, 748, 639, 729 is 1.

HCF(585, 748, 639, 729) = 1

HCF of 585, 748, 639, 729 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 585, 748, 639, 729 is 1.

Highest Common Factor of 585,748,639,729 using Euclid's algorithm

Highest Common Factor of 585,748,639,729 is 1

Step 1: Since 748 > 585, we apply the division lemma to 748 and 585, to get

748 = 585 x 1 + 163

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 163 and 585, to get

585 = 163 x 3 + 96

Step 3: We consider the new divisor 163 and the new remainder 96, and apply the division lemma to get

163 = 96 x 1 + 67

We consider the new divisor 96 and the new remainder 67,and apply the division lemma to get

96 = 67 x 1 + 29

We consider the new divisor 67 and the new remainder 29,and apply the division lemma to get

67 = 29 x 2 + 9

We consider the new divisor 29 and the new remainder 9,and apply the division lemma to get

29 = 9 x 3 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 585 and 748 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(29,9) = HCF(67,29) = HCF(96,67) = HCF(163,96) = HCF(585,163) = HCF(748,585) .

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

Step 1: Since 639 > 1, we apply the division lemma to 639 and 1, to get

639 = 1 x 639 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 639 is 1

Notice that 1 = HCF(639,1) .

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

Step 1: Since 729 > 1, we apply the division lemma to 729 and 1, to get

729 = 1 x 729 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 729 is 1

Notice that 1 = HCF(729,1) .

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Frequently Asked Questions on HCF of 585, 748, 639, 729 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 585, 748, 639, 729?

Answer: HCF of 585, 748, 639, 729 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 748, 639, 729 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 748, 639, 729 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.