Highest Common Factor of 600, 8530, 1541 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 600, 8530, 1541 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 600, 8530, 1541 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 600, 8530, 1541 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 600, 8530, 1541 is 1.

HCF(600, 8530, 1541) = 1

HCF of 600, 8530, 1541 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 600, 8530, 1541 is 1.

Highest Common Factor of 600,8530,1541 using Euclid's algorithm

Highest Common Factor of 600,8530,1541 is 1

Step 1: Since 8530 > 600, we apply the division lemma to 8530 and 600, to get

8530 = 600 x 14 + 130

Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 130 and 600, to get

600 = 130 x 4 + 80

Step 3: We consider the new divisor 130 and the new remainder 80, and apply the division lemma to get

130 = 80 x 1 + 50

We consider the new divisor 80 and the new remainder 50,and apply the division lemma to get

80 = 50 x 1 + 30

We consider the new divisor 50 and the new remainder 30,and apply the division lemma to get

50 = 30 x 1 + 20

We consider the new divisor 30 and the new remainder 20,and apply the division lemma to get

30 = 20 x 1 + 10

We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 600 and 8530 is 10

Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(50,30) = HCF(80,50) = HCF(130,80) = HCF(600,130) = HCF(8530,600) .

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

Step 1: Since 1541 > 10, we apply the division lemma to 1541 and 10, to get

1541 = 10 x 154 + 1

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 1 and 10, to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 1541 is 1

Notice that 1 = HCF(10,1) = HCF(1541,10) .

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Frequently Asked Questions on HCF of 600, 8530, 1541 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 600, 8530, 1541?

Answer: HCF of 600, 8530, 1541 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 600, 8530, 1541 using Euclid's Algorithm?

Answer: For arbitrary numbers 600, 8530, 1541 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.