Highest Common Factor of 360, 590, 747 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 360, 590, 747 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 360, 590, 747 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 360, 590, 747 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 360, 590, 747 is 1.

HCF(360, 590, 747) = 1

HCF of 360, 590, 747 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 360, 590, 747 is 1.

Highest Common Factor of 360,590,747 using Euclid's algorithm

Highest Common Factor of 360,590,747 is 1

Step 1: Since 590 > 360, we apply the division lemma to 590 and 360, to get

590 = 360 x 1 + 230

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 230 and 360, to get

360 = 230 x 1 + 130

Step 3: We consider the new divisor 230 and the new remainder 130, and apply the division lemma to get

230 = 130 x 1 + 100

We consider the new divisor 130 and the new remainder 100,and apply the division lemma to get

130 = 100 x 1 + 30

We consider the new divisor 100 and the new remainder 30,and apply the division lemma to get

100 = 30 x 3 + 10

We consider the new divisor 30 and the new remainder 10,and apply the division lemma to get

30 = 10 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 360 and 590 is 10

Notice that 10 = HCF(30,10) = HCF(100,30) = HCF(130,100) = HCF(230,130) = HCF(360,230) = HCF(590,360) .

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

Step 1: Since 747 > 10, we apply the division lemma to 747 and 10, to get

747 = 10 x 74 + 7

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 7 and 10, to get

10 = 7 x 1 + 3

Step 3: We consider the new divisor 7 and the new remainder 3, and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 10 and 747 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(747,10) .

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Frequently Asked Questions on HCF of 360, 590, 747 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 360, 590, 747?

Answer: HCF of 360, 590, 747 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 360, 590, 747 using Euclid's Algorithm?

Answer: For arbitrary numbers 360, 590, 747 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.