Highest Common Factor of 4190, 1712, 16605 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 4190, 1712, 16605 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 4190, 1712, 16605 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 4190, 1712, 16605 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 4190, 1712, 16605 is 1.

HCF(4190, 1712, 16605) = 1

HCF of 4190, 1712, 16605 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 4190, 1712, 16605 is 1.

Highest Common Factor of 4190,1712,16605 using Euclid's algorithm

Highest Common Factor of 4190,1712,16605 is 1

Step 1: Since 4190 > 1712, we apply the division lemma to 4190 and 1712, to get

4190 = 1712 x 2 + 766

Step 2: Since the reminder 1712 ≠ 0, we apply division lemma to 766 and 1712, to get

1712 = 766 x 2 + 180

Step 3: We consider the new divisor 766 and the new remainder 180, and apply the division lemma to get

766 = 180 x 4 + 46

We consider the new divisor 180 and the new remainder 46,and apply the division lemma to get

180 = 46 x 3 + 42

We consider the new divisor 46 and the new remainder 42,and apply the division lemma to get

46 = 42 x 1 + 4

We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get

42 = 4 x 10 + 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 4190 and 1712 is 2

Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(46,42) = HCF(180,46) = HCF(766,180) = HCF(1712,766) = HCF(4190,1712) .

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

Step 1: Since 16605 > 2, we apply the division lemma to 16605 and 2, to get

16605 = 2 x 8302 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 16605 is 1

Notice that 1 = HCF(2,1) = HCF(16605,2) .

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Frequently Asked Questions on HCF of 4190, 1712, 16605 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 4190, 1712, 16605?

Answer: HCF of 4190, 1712, 16605 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 4190, 1712, 16605 using Euclid's Algorithm?

Answer: For arbitrary numbers 4190, 1712, 16605 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.