Highest Common Factor of 904, 345, 355 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 904, 345, 355 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 904, 345, 355 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 904, 345, 355 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 904, 345, 355 is 1.

HCF(904, 345, 355) = 1

HCF of 904, 345, 355 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 904, 345, 355 is 1.

Highest Common Factor of 904,345,355 using Euclid's algorithm

Highest Common Factor of 904,345,355 is 1

Step 1: Since 904 > 345, we apply the division lemma to 904 and 345, to get

904 = 345 x 2 + 214

Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 214 and 345, to get

345 = 214 x 1 + 131

Step 3: We consider the new divisor 214 and the new remainder 131, and apply the division lemma to get

214 = 131 x 1 + 83

We consider the new divisor 131 and the new remainder 83,and apply the division lemma to get

131 = 83 x 1 + 48

We consider the new divisor 83 and the new remainder 48,and apply the division lemma to get

83 = 48 x 1 + 35

We consider the new divisor 48 and the new remainder 35,and apply the division lemma to get

48 = 35 x 1 + 13

We consider the new divisor 35 and the new remainder 13,and apply the division lemma to get

35 = 13 x 2 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

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 904 and 345 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(35,13) = HCF(48,35) = HCF(83,48) = HCF(131,83) = HCF(214,131) = HCF(345,214) = HCF(904,345) .

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

Step 1: Since 355 > 1, we apply the division lemma to 355 and 1, to get

355 = 1 x 355 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 355 is 1

Notice that 1 = HCF(355,1) .

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Frequently Asked Questions on HCF of 904, 345, 355 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 904, 345, 355?

Answer: HCF of 904, 345, 355 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 904, 345, 355 using Euclid's Algorithm?

Answer: For arbitrary numbers 904, 345, 355 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.