Highest Common Factor of 675, 415, 34 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 675, 415, 34 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 415, 34 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 675, 415, 34 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 675, 415, 34 is 1.

HCF(675, 415, 34) = 1

HCF of 675, 415, 34 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 675, 415, 34 is 1.

Highest Common Factor of 675,415,34 using Euclid's algorithm

Highest Common Factor of 675,415,34 is 1

Step 1: Since 675 > 415, we apply the division lemma to 675 and 415, to get

675 = 415 x 1 + 260

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 260 and 415, to get

415 = 260 x 1 + 155

Step 3: We consider the new divisor 260 and the new remainder 155, and apply the division lemma to get

260 = 155 x 1 + 105

We consider the new divisor 155 and the new remainder 105,and apply the division lemma to get

155 = 105 x 1 + 50

We consider the new divisor 105 and the new remainder 50,and apply the division lemma to get

105 = 50 x 2 + 5

We consider the new divisor 50 and the new remainder 5,and apply the division lemma to get

50 = 5 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 675 and 415 is 5

Notice that 5 = HCF(50,5) = HCF(105,50) = HCF(155,105) = HCF(260,155) = HCF(415,260) = HCF(675,415) .

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

Step 1: Since 34 > 5, we apply the division lemma to 34 and 5, to get

34 = 5 x 6 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 34 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(34,5) .

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Frequently Asked Questions on HCF of 675, 415, 34 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 675, 415, 34?

Answer: HCF of 675, 415, 34 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 415, 34 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 415, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.