Highest Common Factor of 2265, 3350, 10916 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 2265, 3350, 10916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2265, 3350, 10916 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 2265, 3350, 10916 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 2265, 3350, 10916 is 1.

HCF(2265, 3350, 10916) = 1

HCF of 2265, 3350, 10916 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 2265, 3350, 10916 is 1.

Highest Common Factor of 2265,3350,10916 using Euclid's algorithm

Highest Common Factor of 2265,3350,10916 is 1

Step 1: Since 3350 > 2265, we apply the division lemma to 3350 and 2265, to get

3350 = 2265 x 1 + 1085

Step 2: Since the reminder 2265 ≠ 0, we apply division lemma to 1085 and 2265, to get

2265 = 1085 x 2 + 95

Step 3: We consider the new divisor 1085 and the new remainder 95, and apply the division lemma to get

1085 = 95 x 11 + 40

We consider the new divisor 95 and the new remainder 40,and apply the division lemma to get

95 = 40 x 2 + 15

We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get

40 = 15 x 2 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 2265 and 3350 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(95,40) = HCF(1085,95) = HCF(2265,1085) = HCF(3350,2265) .

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

Step 1: Since 10916 > 5, we apply the division lemma to 10916 and 5, to get

10916 = 5 x 2183 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 10916 is 1

Notice that 1 = HCF(5,1) = HCF(10916,5) .

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Frequently Asked Questions on HCF of 2265, 3350, 10916 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 2265, 3350, 10916?

Answer: HCF of 2265, 3350, 10916 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2265, 3350, 10916 using Euclid's Algorithm?

Answer: For arbitrary numbers 2265, 3350, 10916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.