Highest Common Factor of 644, 474, 414 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 644, 474, 414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 644, 474, 414 is 2 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 644, 474, 414 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 644, 474, 414 is 2.

HCF(644, 474, 414) = 2

HCF of 644, 474, 414 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 644, 474, 414 is 2.

Highest Common Factor of 644,474,414 using Euclid's algorithm

Highest Common Factor of 644,474,414 is 2

Step 1: Since 644 > 474, we apply the division lemma to 644 and 474, to get

644 = 474 x 1 + 170

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 170 and 474, to get

474 = 170 x 2 + 134

Step 3: We consider the new divisor 170 and the new remainder 134, and apply the division lemma to get

170 = 134 x 1 + 36

We consider the new divisor 134 and the new remainder 36,and apply the division lemma to get

134 = 36 x 3 + 26

We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get

36 = 26 x 1 + 10

We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get

26 = 10 x 2 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 644 and 474 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(134,36) = HCF(170,134) = HCF(474,170) = HCF(644,474) .

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

Step 1: Since 414 > 2, we apply the division lemma to 414 and 2, to get

414 = 2 x 207 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 414 is 2

Notice that 2 = HCF(414,2) .

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Frequently Asked Questions on HCF of 644, 474, 414 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 644, 474, 414?

Answer: HCF of 644, 474, 414 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 644, 474, 414 using Euclid's Algorithm?

Answer: For arbitrary numbers 644, 474, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.