Highest Common Factor of 415, 775, 322 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 415, 775, 322 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 415, 775, 322 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 415, 775, 322 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 415, 775, 322 is 1.

HCF(415, 775, 322) = 1

HCF of 415, 775, 322 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 415, 775, 322 is 1.

Highest Common Factor of 415,775,322 using Euclid's algorithm

Highest Common Factor of 415,775,322 is 1

Step 1: Since 775 > 415, we apply the division lemma to 775 and 415, to get

775 = 415 x 1 + 360

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 360 and 415, to get

415 = 360 x 1 + 55

Step 3: We consider the new divisor 360 and the new remainder 55, and apply the division lemma to get

360 = 55 x 6 + 30

We consider the new divisor 55 and the new remainder 30,and apply the division lemma to get

55 = 30 x 1 + 25

We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get

30 = 25 x 1 + 5

We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 415 and 775 is 5

Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(55,30) = HCF(360,55) = HCF(415,360) = HCF(775,415) .

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

Step 1: Since 322 > 5, we apply the division lemma to 322 and 5, to get

322 = 5 x 64 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 322 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(322,5) .

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Frequently Asked Questions on HCF of 415, 775, 322 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 415, 775, 322?

Answer: HCF of 415, 775, 322 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 415, 775, 322 using Euclid's Algorithm?

Answer: For arbitrary numbers 415, 775, 322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.