Highest Common Factor of 1737, 6626 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 1737, 6626 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1737, 6626 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 1737, 6626 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 1737, 6626 is 1.

HCF(1737, 6626) = 1

HCF of 1737, 6626 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 1737, 6626 is 1.

Highest Common Factor of 1737,6626 using Euclid's algorithm

Highest Common Factor of 1737,6626 is 1

Step 1: Since 6626 > 1737, we apply the division lemma to 6626 and 1737, to get

6626 = 1737 x 3 + 1415

Step 2: Since the reminder 1737 ≠ 0, we apply division lemma to 1415 and 1737, to get

1737 = 1415 x 1 + 322

Step 3: We consider the new divisor 1415 and the new remainder 322, and apply the division lemma to get

1415 = 322 x 4 + 127

We consider the new divisor 322 and the new remainder 127,and apply the division lemma to get

322 = 127 x 2 + 68

We consider the new divisor 127 and the new remainder 68,and apply the division lemma to get

127 = 68 x 1 + 59

We consider the new divisor 68 and the new remainder 59,and apply the division lemma to get

68 = 59 x 1 + 9

We consider the new divisor 59 and the new remainder 9,and apply the division lemma to get

59 = 9 x 6 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

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 1737 and 6626 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(59,9) = HCF(68,59) = HCF(127,68) = HCF(322,127) = HCF(1415,322) = HCF(1737,1415) = HCF(6626,1737) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 1737, 6626 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 1737, 6626?

Answer: HCF of 1737, 6626 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1737, 6626 using Euclid's Algorithm?

Answer: For arbitrary numbers 1737, 6626 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.