Highest Common Factor of 345, 544, 406 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 345, 544, 406 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 345, 544, 406 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 345, 544, 406 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 345, 544, 406 is 1.

HCF(345, 544, 406) = 1

HCF of 345, 544, 406 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 345, 544, 406 is 1.

Highest Common Factor of 345,544,406 using Euclid's algorithm

Highest Common Factor of 345,544,406 is 1

Step 1: Since 544 > 345, we apply the division lemma to 544 and 345, to get

544 = 345 x 1 + 199

Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 199 and 345, to get

345 = 199 x 1 + 146

Step 3: We consider the new divisor 199 and the new remainder 146, and apply the division lemma to get

199 = 146 x 1 + 53

We consider the new divisor 146 and the new remainder 53,and apply the division lemma to get

146 = 53 x 2 + 40

We consider the new divisor 53 and the new remainder 40,and apply the division lemma to get

53 = 40 x 1 + 13

We consider the new divisor 40 and the new remainder 13,and apply the division lemma to get

40 = 13 x 3 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 345 and 544 is 1

Notice that 1 = HCF(13,1) = HCF(40,13) = HCF(53,40) = HCF(146,53) = HCF(199,146) = HCF(345,199) = HCF(544,345) .

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

Step 1: Since 406 > 1, we apply the division lemma to 406 and 1, to get

406 = 1 x 406 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 406 is 1

Notice that 1 = HCF(406,1) .

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Frequently Asked Questions on HCF of 345, 544, 406 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 345, 544, 406?

Answer: HCF of 345, 544, 406 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 345, 544, 406 using Euclid's Algorithm?

Answer: For arbitrary numbers 345, 544, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.