Highest Common Factor of 1646, 6001 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 1646, 6001 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1646, 6001 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 1646, 6001 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 1646, 6001 is 1.

HCF(1646, 6001) = 1

HCF of 1646, 6001 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 1646, 6001 is 1.

Highest Common Factor of 1646,6001 using Euclid's algorithm

Highest Common Factor of 1646,6001 is 1

Step 1: Since 6001 > 1646, we apply the division lemma to 6001 and 1646, to get

6001 = 1646 x 3 + 1063

Step 2: Since the reminder 1646 ≠ 0, we apply division lemma to 1063 and 1646, to get

1646 = 1063 x 1 + 583

Step 3: We consider the new divisor 1063 and the new remainder 583, and apply the division lemma to get

1063 = 583 x 1 + 480

We consider the new divisor 583 and the new remainder 480,and apply the division lemma to get

583 = 480 x 1 + 103

We consider the new divisor 480 and the new remainder 103,and apply the division lemma to get

480 = 103 x 4 + 68

We consider the new divisor 103 and the new remainder 68,and apply the division lemma to get

103 = 68 x 1 + 35

We consider the new divisor 68 and the new remainder 35,and apply the division lemma to get

68 = 35 x 1 + 33

We consider the new divisor 35 and the new remainder 33,and apply the division lemma to get

35 = 33 x 1 + 2

We consider the new divisor 33 and the new remainder 2,and apply the division lemma to get

33 = 2 x 16 + 1

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 1646 and 6001 is 1

Notice that 1 = HCF(2,1) = HCF(33,2) = HCF(35,33) = HCF(68,35) = HCF(103,68) = HCF(480,103) = HCF(583,480) = HCF(1063,583) = HCF(1646,1063) = HCF(6001,1646) .

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Frequently Asked Questions on HCF of 1646, 6001 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 1646, 6001?

Answer: HCF of 1646, 6001 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1646, 6001 using Euclid's Algorithm?

Answer: For arbitrary numbers 1646, 6001 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.