Highest Common Factor of 600, 389, 69 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, 389, 69 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 600, 389, 69 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, 389, 69 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, 389, 69 is 1.

HCF(600, 389, 69) = 1

HCF of 600, 389, 69 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, 389, 69 is 1.

Highest Common Factor of 600,389,69 using Euclid's algorithm

Highest Common Factor of 600,389,69 is 1

Step 1: Since 600 > 389, we apply the division lemma to 600 and 389, to get

600 = 389 x 1 + 211

Step 2: Since the reminder 389 ≠ 0, we apply division lemma to 211 and 389, to get

389 = 211 x 1 + 178

Step 3: We consider the new divisor 211 and the new remainder 178, and apply the division lemma to get

211 = 178 x 1 + 33

We consider the new divisor 178 and the new remainder 33,and apply the division lemma to get

178 = 33 x 5 + 13

We consider the new divisor 33 and the new remainder 13,and apply the division lemma to get

33 = 13 x 2 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 600 and 389 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(33,13) = HCF(178,33) = HCF(211,178) = HCF(389,211) = HCF(600,389) .

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

Step 1: Since 69 > 1, we apply the division lemma to 69 and 1, to get

69 = 1 x 69 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 69 is 1

Notice that 1 = HCF(69,1) .

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Frequently Asked Questions on HCF of 600, 389, 69 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, 389, 69?

Answer: HCF of 600, 389, 69 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 600, 389, 69 using Euclid's Algorithm?

Answer: For arbitrary numbers 600, 389, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.