Highest Common Factor of 604, 130, 269 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 604, 130, 269 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 604, 130, 269 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 604, 130, 269 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 604, 130, 269 is 1.

HCF(604, 130, 269) = 1

HCF of 604, 130, 269 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 604, 130, 269 is 1.

Highest Common Factor of 604,130,269 using Euclid's algorithm

Highest Common Factor of 604,130,269 is 1

Step 1: Since 604 > 130, we apply the division lemma to 604 and 130, to get

604 = 130 x 4 + 84

Step 2: Since the reminder 130 ≠ 0, we apply division lemma to 84 and 130, to get

130 = 84 x 1 + 46

Step 3: We consider the new divisor 84 and the new remainder 46, and apply the division lemma to get

84 = 46 x 1 + 38

We consider the new divisor 46 and the new remainder 38,and apply the division lemma to get

46 = 38 x 1 + 8

We consider the new divisor 38 and the new remainder 8,and apply the division lemma to get

38 = 8 x 4 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 604 and 130 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(46,38) = HCF(84,46) = HCF(130,84) = HCF(604,130) .

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

Step 1: Since 269 > 2, we apply the division lemma to 269 and 2, to get

269 = 2 x 134 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 269 is 1

Notice that 1 = HCF(2,1) = HCF(269,2) .

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Frequently Asked Questions on HCF of 604, 130, 269 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 604, 130, 269?

Answer: HCF of 604, 130, 269 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 604, 130, 269 using Euclid's Algorithm?

Answer: For arbitrary numbers 604, 130, 269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.