Highest Common Factor of 565, 911, 670 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 565, 911, 670 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 565, 911, 670 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 565, 911, 670 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 565, 911, 670 is 1.

HCF(565, 911, 670) = 1

HCF of 565, 911, 670 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 565, 911, 670 is 1.

Highest Common Factor of 565,911,670 using Euclid's algorithm

Highest Common Factor of 565,911,670 is 1

Step 1: Since 911 > 565, we apply the division lemma to 911 and 565, to get

911 = 565 x 1 + 346

Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 346 and 565, to get

565 = 346 x 1 + 219

Step 3: We consider the new divisor 346 and the new remainder 219, and apply the division lemma to get

346 = 219 x 1 + 127

We consider the new divisor 219 and the new remainder 127,and apply the division lemma to get

219 = 127 x 1 + 92

We consider the new divisor 127 and the new remainder 92,and apply the division lemma to get

127 = 92 x 1 + 35

We consider the new divisor 92 and the new remainder 35,and apply the division lemma to get

92 = 35 x 2 + 22

We consider the new divisor 35 and the new remainder 22,and apply the division lemma to get

35 = 22 x 1 + 13

We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get

22 = 13 x 1 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 565 and 911 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(35,22) = HCF(92,35) = HCF(127,92) = HCF(219,127) = HCF(346,219) = HCF(565,346) = HCF(911,565) .

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

Step 1: Since 670 > 1, we apply the division lemma to 670 and 1, to get

670 = 1 x 670 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 670 is 1

Notice that 1 = HCF(670,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 565, 911, 670 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 565, 911, 670?

Answer: HCF of 565, 911, 670 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 565, 911, 670 using Euclid's Algorithm?

Answer: For arbitrary numbers 565, 911, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.