Highest Common Factor of 1007, 1661 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 1007, 1661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1007, 1661 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 1007, 1661 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 1007, 1661 is 1.

HCF(1007, 1661) = 1

HCF of 1007, 1661 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 1007, 1661 is 1.

Highest Common Factor of 1007,1661 using Euclid's algorithm

Highest Common Factor of 1007,1661 is 1

Step 1: Since 1661 > 1007, we apply the division lemma to 1661 and 1007, to get

1661 = 1007 x 1 + 654

Step 2: Since the reminder 1007 ≠ 0, we apply division lemma to 654 and 1007, to get

1007 = 654 x 1 + 353

Step 3: We consider the new divisor 654 and the new remainder 353, and apply the division lemma to get

654 = 353 x 1 + 301

We consider the new divisor 353 and the new remainder 301,and apply the division lemma to get

353 = 301 x 1 + 52

We consider the new divisor 301 and the new remainder 52,and apply the division lemma to get

301 = 52 x 5 + 41

We consider the new divisor 52 and the new remainder 41,and apply the division lemma to get

52 = 41 x 1 + 11

We consider the new divisor 41 and the new remainder 11,and apply the division lemma to get

41 = 11 x 3 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 1007 and 1661 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(41,11) = HCF(52,41) = HCF(301,52) = HCF(353,301) = HCF(654,353) = HCF(1007,654) = HCF(1661,1007) .

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Frequently Asked Questions on HCF of 1007, 1661 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 1007, 1661?

Answer: HCF of 1007, 1661 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1007, 1661 using Euclid's Algorithm?

Answer: For arbitrary numbers 1007, 1661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.