Highest Common Factor of 3713, 7606, 35993 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 3713, 7606, 35993 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3713, 7606, 35993 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 3713, 7606, 35993 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 3713, 7606, 35993 is 1.

HCF(3713, 7606, 35993) = 1

HCF of 3713, 7606, 35993 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 3713, 7606, 35993 is 1.

Highest Common Factor of 3713,7606,35993 using Euclid's algorithm

Highest Common Factor of 3713,7606,35993 is 1

Step 1: Since 7606 > 3713, we apply the division lemma to 7606 and 3713, to get

7606 = 3713 x 2 + 180

Step 2: Since the reminder 3713 ≠ 0, we apply division lemma to 180 and 3713, to get

3713 = 180 x 20 + 113

Step 3: We consider the new divisor 180 and the new remainder 113, and apply the division lemma to get

180 = 113 x 1 + 67

We consider the new divisor 113 and the new remainder 67,and apply the division lemma to get

113 = 67 x 1 + 46

We consider the new divisor 67 and the new remainder 46,and apply the division lemma to get

67 = 46 x 1 + 21

We consider the new divisor 46 and the new remainder 21,and apply the division lemma to get

46 = 21 x 2 + 4

We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get

21 = 4 x 5 + 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 3713 and 7606 is 1

Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(46,21) = HCF(67,46) = HCF(113,67) = HCF(180,113) = HCF(3713,180) = HCF(7606,3713) .

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

Step 1: Since 35993 > 1, we apply the division lemma to 35993 and 1, to get

35993 = 1 x 35993 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 35993 is 1

Notice that 1 = HCF(35993,1) .

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Frequently Asked Questions on HCF of 3713, 7606, 35993 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 3713, 7606, 35993?

Answer: HCF of 3713, 7606, 35993 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3713, 7606, 35993 using Euclid's Algorithm?

Answer: For arbitrary numbers 3713, 7606, 35993 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.