Highest Common Factor of 6909, 9874, 91569 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 6909, 9874, 91569 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6909, 9874, 91569 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 6909, 9874, 91569 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 6909, 9874, 91569 is 1.

HCF(6909, 9874, 91569) = 1

HCF of 6909, 9874, 91569 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 6909, 9874, 91569 is 1.

Highest Common Factor of 6909,9874,91569 using Euclid's algorithm

Highest Common Factor of 6909,9874,91569 is 1

Step 1: Since 9874 > 6909, we apply the division lemma to 9874 and 6909, to get

9874 = 6909 x 1 + 2965

Step 2: Since the reminder 6909 ≠ 0, we apply division lemma to 2965 and 6909, to get

6909 = 2965 x 2 + 979

Step 3: We consider the new divisor 2965 and the new remainder 979, and apply the division lemma to get

2965 = 979 x 3 + 28

We consider the new divisor 979 and the new remainder 28,and apply the division lemma to get

979 = 28 x 34 + 27

We consider the new divisor 28 and the new remainder 27,and apply the division lemma to get

28 = 27 x 1 + 1

We consider the new divisor 27 and the new remainder 1,and apply the division lemma to get

27 = 1 x 27 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6909 and 9874 is 1

Notice that 1 = HCF(27,1) = HCF(28,27) = HCF(979,28) = HCF(2965,979) = HCF(6909,2965) = HCF(9874,6909) .

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

Step 1: Since 91569 > 1, we apply the division lemma to 91569 and 1, to get

91569 = 1 x 91569 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 91569 is 1

Notice that 1 = HCF(91569,1) .

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Frequently Asked Questions on HCF of 6909, 9874, 91569 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 6909, 9874, 91569?

Answer: HCF of 6909, 9874, 91569 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6909, 9874, 91569 using Euclid's Algorithm?

Answer: For arbitrary numbers 6909, 9874, 91569 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.