Highest Common Factor of 705, 250, 346 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 705, 250, 346 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 705, 250, 346 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 705, 250, 346 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 705, 250, 346 is 1.

HCF(705, 250, 346) = 1

HCF of 705, 250, 346 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 705, 250, 346 is 1.

Highest Common Factor of 705,250,346 using Euclid's algorithm

Highest Common Factor of 705,250,346 is 1

Step 1: Since 705 > 250, we apply the division lemma to 705 and 250, to get

705 = 250 x 2 + 205

Step 2: Since the reminder 250 ≠ 0, we apply division lemma to 205 and 250, to get

250 = 205 x 1 + 45

Step 3: We consider the new divisor 205 and the new remainder 45, and apply the division lemma to get

205 = 45 x 4 + 25

We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get

45 = 25 x 1 + 20

We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get

25 = 20 x 1 + 5

We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 705 and 250 is 5

Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(205,45) = HCF(250,205) = HCF(705,250) .

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

Step 1: Since 346 > 5, we apply the division lemma to 346 and 5, to get

346 = 5 x 69 + 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 346 is 1

Notice that 1 = HCF(5,1) = HCF(346,5) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 705, 250, 346 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 705, 250, 346?

Answer: HCF of 705, 250, 346 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 705, 250, 346 using Euclid's Algorithm?

Answer: For arbitrary numbers 705, 250, 346 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.