Highest Common Factor of 9405, 2156, 34177 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 9405, 2156, 34177 i.e. 11 the largest integer that leaves a remainder zero for all numbers.

HCF of 9405, 2156, 34177 is 11 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 9405, 2156, 34177 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 9405, 2156, 34177 is 11.

HCF(9405, 2156, 34177) = 11

HCF of 9405, 2156, 34177 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 9405, 2156, 34177 is 11.

Highest Common Factor of 9405,2156,34177 using Euclid's algorithm

Highest Common Factor of 9405,2156,34177 is 11

Step 1: Since 9405 > 2156, we apply the division lemma to 9405 and 2156, to get

9405 = 2156 x 4 + 781

Step 2: Since the reminder 2156 ≠ 0, we apply division lemma to 781 and 2156, to get

2156 = 781 x 2 + 594

Step 3: We consider the new divisor 781 and the new remainder 594, and apply the division lemma to get

781 = 594 x 1 + 187

We consider the new divisor 594 and the new remainder 187,and apply the division lemma to get

594 = 187 x 3 + 33

We consider the new divisor 187 and the new remainder 33,and apply the division lemma to get

187 = 33 x 5 + 22

We consider the new divisor 33 and the new remainder 22,and apply the division lemma to get

33 = 22 x 1 + 11

We consider the new divisor 22 and the new remainder 11,and apply the division lemma to get

22 = 11 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 9405 and 2156 is 11

Notice that 11 = HCF(22,11) = HCF(33,22) = HCF(187,33) = HCF(594,187) = HCF(781,594) = HCF(2156,781) = HCF(9405,2156) .

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

Step 1: Since 34177 > 11, we apply the division lemma to 34177 and 11, to get

34177 = 11 x 3107 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 11 and 34177 is 11

Notice that 11 = HCF(34177,11) .

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Frequently Asked Questions on HCF of 9405, 2156, 34177 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 9405, 2156, 34177?

Answer: HCF of 9405, 2156, 34177 is 11 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9405, 2156, 34177 using Euclid's Algorithm?

Answer: For arbitrary numbers 9405, 2156, 34177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.