Highest Common Factor of 410, 660, 349 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 410, 660, 349 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 410, 660, 349 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 410, 660, 349 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 410, 660, 349 is 1.

HCF(410, 660, 349) = 1

HCF of 410, 660, 349 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 410, 660, 349 is 1.

Highest Common Factor of 410,660,349 using Euclid's algorithm

Highest Common Factor of 410,660,349 is 1

Step 1: Since 660 > 410, we apply the division lemma to 660 and 410, to get

660 = 410 x 1 + 250

Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 250 and 410, to get

410 = 250 x 1 + 160

Step 3: We consider the new divisor 250 and the new remainder 160, and apply the division lemma to get

250 = 160 x 1 + 90

We consider the new divisor 160 and the new remainder 90,and apply the division lemma to get

160 = 90 x 1 + 70

We consider the new divisor 90 and the new remainder 70,and apply the division lemma to get

90 = 70 x 1 + 20

We consider the new divisor 70 and the new remainder 20,and apply the division lemma to get

70 = 20 x 3 + 10

We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 410 and 660 is 10

Notice that 10 = HCF(20,10) = HCF(70,20) = HCF(90,70) = HCF(160,90) = HCF(250,160) = HCF(410,250) = HCF(660,410) .

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

Step 1: Since 349 > 10, we apply the division lemma to 349 and 10, to get

349 = 10 x 34 + 9

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 9 and 10, to get

10 = 9 x 1 + 1

Step 3: We consider the new divisor 9 and the new remainder 1, and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 349 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(349,10) .

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Frequently Asked Questions on HCF of 410, 660, 349 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 410, 660, 349?

Answer: HCF of 410, 660, 349 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 410, 660, 349 using Euclid's Algorithm?

Answer: For arbitrary numbers 410, 660, 349 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.