Highest Common Factor of 685, 950, 209, 46 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 685, 950, 209, 46 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 950, 209, 46 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 685, 950, 209, 46 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 685, 950, 209, 46 is 1.

HCF(685, 950, 209, 46) = 1

HCF of 685, 950, 209, 46 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 685, 950, 209, 46 is 1.

Highest Common Factor of 685,950,209,46 using Euclid's algorithm

Highest Common Factor of 685,950,209,46 is 1

Step 1: Since 950 > 685, we apply the division lemma to 950 and 685, to get

950 = 685 x 1 + 265

Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 265 and 685, to get

685 = 265 x 2 + 155

Step 3: We consider the new divisor 265 and the new remainder 155, and apply the division lemma to get

265 = 155 x 1 + 110

We consider the new divisor 155 and the new remainder 110,and apply the division lemma to get

155 = 110 x 1 + 45

We consider the new divisor 110 and the new remainder 45,and apply the division lemma to get

110 = 45 x 2 + 20

We consider the new divisor 45 and the new remainder 20,and apply the division lemma to get

45 = 20 x 2 + 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 685 and 950 is 5

Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(110,45) = HCF(155,110) = HCF(265,155) = HCF(685,265) = HCF(950,685) .

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

Step 1: Since 209 > 5, we apply the division lemma to 209 and 5, to get

209 = 5 x 41 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: 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 5 and 209 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(209,5) .

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

Step 1: Since 46 > 1, we apply the division lemma to 46 and 1, to get

46 = 1 x 46 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 46 is 1

Notice that 1 = HCF(46,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 685, 950, 209, 46 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 685, 950, 209, 46?

Answer: HCF of 685, 950, 209, 46 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 950, 209, 46 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 950, 209, 46 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.