Highest Common Factor of 419, 674, 474 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 419, 674, 474 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 674, 474 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 419, 674, 474 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 419, 674, 474 is 1.

HCF(419, 674, 474) = 1

HCF of 419, 674, 474 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 419, 674, 474 is 1.

Highest Common Factor of 419,674,474 using Euclid's algorithm

Highest Common Factor of 419,674,474 is 1

Step 1: Since 674 > 419, we apply the division lemma to 674 and 419, to get

674 = 419 x 1 + 255

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 255 and 419, to get

419 = 255 x 1 + 164

Step 3: We consider the new divisor 255 and the new remainder 164, and apply the division lemma to get

255 = 164 x 1 + 91

We consider the new divisor 164 and the new remainder 91,and apply the division lemma to get

164 = 91 x 1 + 73

We consider the new divisor 91 and the new remainder 73,and apply the division lemma to get

91 = 73 x 1 + 18

We consider the new divisor 73 and the new remainder 18,and apply the division lemma to get

73 = 18 x 4 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 419 and 674 is 1

Notice that 1 = HCF(18,1) = HCF(73,18) = HCF(91,73) = HCF(164,91) = HCF(255,164) = HCF(419,255) = HCF(674,419) .

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

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

474 = 1 x 474 + 0

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

Notice that 1 = HCF(474,1) .

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Frequently Asked Questions on HCF of 419, 674, 474 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 419, 674, 474?

Answer: HCF of 419, 674, 474 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 674, 474 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 674, 474 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.