Highest Common Factor of 1705, 2995, 17452 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 1705, 2995, 17452 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1705, 2995, 17452 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 1705, 2995, 17452 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 1705, 2995, 17452 is 1.

HCF(1705, 2995, 17452) = 1

HCF of 1705, 2995, 17452 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 1705, 2995, 17452 is 1.

Highest Common Factor of 1705,2995,17452 using Euclid's algorithm

Highest Common Factor of 1705,2995,17452 is 1

Step 1: Since 2995 > 1705, we apply the division lemma to 2995 and 1705, to get

2995 = 1705 x 1 + 1290

Step 2: Since the reminder 1705 ≠ 0, we apply division lemma to 1290 and 1705, to get

1705 = 1290 x 1 + 415

Step 3: We consider the new divisor 1290 and the new remainder 415, and apply the division lemma to get

1290 = 415 x 3 + 45

We consider the new divisor 415 and the new remainder 45,and apply the division lemma to get

415 = 45 x 9 + 10

We consider the new divisor 45 and the new remainder 10,and apply the division lemma to get

45 = 10 x 4 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 1705 and 2995 is 5

Notice that 5 = HCF(10,5) = HCF(45,10) = HCF(415,45) = HCF(1290,415) = HCF(1705,1290) = HCF(2995,1705) .

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

Step 1: Since 17452 > 5, we apply the division lemma to 17452 and 5, to get

17452 = 5 x 3490 + 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 17452 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17452,5) .

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Frequently Asked Questions on HCF of 1705, 2995, 17452 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 1705, 2995, 17452?

Answer: HCF of 1705, 2995, 17452 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1705, 2995, 17452 using Euclid's Algorithm?

Answer: For arbitrary numbers 1705, 2995, 17452 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.