Highest Common Factor of 474, 1691, 1419 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 474, 1691, 1419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 474, 1691, 1419 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 474, 1691, 1419 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 474, 1691, 1419 is 1.

HCF(474, 1691, 1419) = 1

HCF of 474, 1691, 1419 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 474, 1691, 1419 is 1.

Highest Common Factor of 474,1691,1419 using Euclid's algorithm

Highest Common Factor of 474,1691,1419 is 1

Step 1: Since 1691 > 474, we apply the division lemma to 1691 and 474, to get

1691 = 474 x 3 + 269

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 269 and 474, to get

474 = 269 x 1 + 205

Step 3: We consider the new divisor 269 and the new remainder 205, and apply the division lemma to get

269 = 205 x 1 + 64

We consider the new divisor 205 and the new remainder 64,and apply the division lemma to get

205 = 64 x 3 + 13

We consider the new divisor 64 and the new remainder 13,and apply the division lemma to get

64 = 13 x 4 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 474 and 1691 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(64,13) = HCF(205,64) = HCF(269,205) = HCF(474,269) = HCF(1691,474) .

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

Step 1: Since 1419 > 1, we apply the division lemma to 1419 and 1, to get

1419 = 1 x 1419 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1419 is 1

Notice that 1 = HCF(1419,1) .

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Frequently Asked Questions on HCF of 474, 1691, 1419 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 474, 1691, 1419?

Answer: HCF of 474, 1691, 1419 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 474, 1691, 1419 using Euclid's Algorithm?

Answer: For arbitrary numbers 474, 1691, 1419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.