Highest Common Factor of 344, 217, 415, 12 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 344, 217, 415, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 344, 217, 415, 12 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 344, 217, 415, 12 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 344, 217, 415, 12 is 1.

HCF(344, 217, 415, 12) = 1

HCF of 344, 217, 415, 12 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 344, 217, 415, 12 is 1.

Highest Common Factor of 344,217,415,12 using Euclid's algorithm

Highest Common Factor of 344,217,415,12 is 1

Step 1: Since 344 > 217, we apply the division lemma to 344 and 217, to get

344 = 217 x 1 + 127

Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 127 and 217, to get

217 = 127 x 1 + 90

Step 3: We consider the new divisor 127 and the new remainder 90, and apply the division lemma to get

127 = 90 x 1 + 37

We consider the new divisor 90 and the new remainder 37,and apply the division lemma to get

90 = 37 x 2 + 16

We consider the new divisor 37 and the new remainder 16,and apply the division lemma to get

37 = 16 x 2 + 5

We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get

16 = 5 x 3 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma 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 344 and 217 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(37,16) = HCF(90,37) = HCF(127,90) = HCF(217,127) = HCF(344,217) .

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

Step 1: Since 415 > 1, we apply the division lemma to 415 and 1, to get

415 = 1 x 415 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 415 is 1

Notice that 1 = HCF(415,1) .

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

Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1

Notice that 1 = HCF(12,1) .

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Frequently Asked Questions on HCF of 344, 217, 415, 12 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 344, 217, 415, 12?

Answer: HCF of 344, 217, 415, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 344, 217, 415, 12 using Euclid's Algorithm?

Answer: For arbitrary numbers 344, 217, 415, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.