Highest Common Factor of 676, 440, 419 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 676, 440, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 676, 440, 419 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 676, 440, 419 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 676, 440, 419 is 1.

HCF(676, 440, 419) = 1

HCF of 676, 440, 419 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 676, 440, 419 is 1.

Highest Common Factor of 676,440,419 using Euclid's algorithm

Highest Common Factor of 676,440,419 is 1

Step 1: Since 676 > 440, we apply the division lemma to 676 and 440, to get

676 = 440 x 1 + 236

Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 236 and 440, to get

440 = 236 x 1 + 204

Step 3: We consider the new divisor 236 and the new remainder 204, and apply the division lemma to get

236 = 204 x 1 + 32

We consider the new divisor 204 and the new remainder 32,and apply the division lemma to get

204 = 32 x 6 + 12

We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get

32 = 12 x 2 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 676 and 440 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(204,32) = HCF(236,204) = HCF(440,236) = HCF(676,440) .

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

Step 1: Since 419 > 4, we apply the division lemma to 419 and 4, to get

419 = 4 x 104 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 419 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(419,4) .

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Frequently Asked Questions on HCF of 676, 440, 419 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 676, 440, 419?

Answer: HCF of 676, 440, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 676, 440, 419 using Euclid's Algorithm?

Answer: For arbitrary numbers 676, 440, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.