Highest Common Factor of 904, 708, 29, 317 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, 708, 29, 317 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 904, 708, 29, 317 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, 708, 29, 317 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, 708, 29, 317 is 1.

HCF(904, 708, 29, 317) = 1

HCF of 904, 708, 29, 317 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, 708, 29, 317 is 1.

Highest Common Factor of 904,708,29,317 using Euclid's algorithm

Highest Common Factor of 904,708,29,317 is 1

Step 1: Since 904 > 708, we apply the division lemma to 904 and 708, to get

904 = 708 x 1 + 196

Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 196 and 708, to get

708 = 196 x 3 + 120

Step 3: We consider the new divisor 196 and the new remainder 120, and apply the division lemma to get

196 = 120 x 1 + 76

We consider the new divisor 120 and the new remainder 76,and apply the division lemma to get

120 = 76 x 1 + 44

We consider the new divisor 76 and the new remainder 44,and apply the division lemma to get

76 = 44 x 1 + 32

We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get

44 = 32 x 1 + 12

We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get

32 = 12 x 2 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 904 and 708 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(76,44) = HCF(120,76) = HCF(196,120) = HCF(708,196) = HCF(904,708) .

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

Step 1: Since 29 > 4, we apply the division lemma to 29 and 4, to get

29 = 4 x 7 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 29 is 1

Notice that 1 = HCF(4,1) = HCF(29,4) .

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

Step 1: Since 317 > 1, we apply the division lemma to 317 and 1, to get

317 = 1 x 317 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 317 is 1

Notice that 1 = HCF(317,1) .

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Frequently Asked Questions on HCF of 904, 708, 29, 317 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, 708, 29, 317?

Answer: HCF of 904, 708, 29, 317 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 904, 708, 29, 317 using Euclid's Algorithm?

Answer: For arbitrary numbers 904, 708, 29, 317 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.