Highest Common Factor of 2170, 9568 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 2170, 9568 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 2170, 9568 is 2 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 2170, 9568 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 2170, 9568 is 2.

HCF(2170, 9568) = 2

HCF of 2170, 9568 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 2170, 9568 is 2.

Highest Common Factor of 2170,9568 using Euclid's algorithm

Highest Common Factor of 2170,9568 is 2

Step 1: Since 9568 > 2170, we apply the division lemma to 9568 and 2170, to get

9568 = 2170 x 4 + 888

Step 2: Since the reminder 2170 ≠ 0, we apply division lemma to 888 and 2170, to get

2170 = 888 x 2 + 394

Step 3: We consider the new divisor 888 and the new remainder 394, and apply the division lemma to get

888 = 394 x 2 + 100

We consider the new divisor 394 and the new remainder 100,and apply the division lemma to get

394 = 100 x 3 + 94

We consider the new divisor 100 and the new remainder 94,and apply the division lemma to get

100 = 94 x 1 + 6

We consider the new divisor 94 and the new remainder 6,and apply the division lemma to get

94 = 6 x 15 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2170 and 9568 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(94,6) = HCF(100,94) = HCF(394,100) = HCF(888,394) = HCF(2170,888) = HCF(9568,2170) .

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Frequently Asked Questions on HCF of 2170, 9568 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 2170, 9568?

Answer: HCF of 2170, 9568 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2170, 9568 using Euclid's Algorithm?

Answer: For arbitrary numbers 2170, 9568 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.