Highest Common Factor of 600, 648, 859 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, 648, 859 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 600, 648, 859 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, 648, 859 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, 648, 859 is 1.

HCF(600, 648, 859) = 1

HCF of 600, 648, 859 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, 648, 859 is 1.

Highest Common Factor of 600,648,859 using Euclid's algorithm

Highest Common Factor of 600,648,859 is 1

Step 1: Since 648 > 600, we apply the division lemma to 648 and 600, to get

648 = 600 x 1 + 48

Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 48 and 600, to get

600 = 48 x 12 + 24

Step 3: We consider the new divisor 48 and the new remainder 24, and apply the division lemma to get

48 = 24 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 600 and 648 is 24

Notice that 24 = HCF(48,24) = HCF(600,48) = HCF(648,600) .

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

Step 1: Since 859 > 24, we apply the division lemma to 859 and 24, to get

859 = 24 x 35 + 19

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 19 and 24, to get

24 = 19 x 1 + 5

Step 3: We consider the new divisor 19 and the new remainder 5, and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 24 and 859 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(859,24) .

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Frequently Asked Questions on HCF of 600, 648, 859 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, 648, 859?

Answer: HCF of 600, 648, 859 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 600, 648, 859 using Euclid's Algorithm?

Answer: For arbitrary numbers 600, 648, 859 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.