Highest Common Factor of 906, 708, 994 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 906, 708, 994 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 906, 708, 994 is 2 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 906, 708, 994 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 906, 708, 994 is 2.

HCF(906, 708, 994) = 2

HCF of 906, 708, 994 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 906, 708, 994 is 2.

Highest Common Factor of 906,708,994 using Euclid's algorithm

Highest Common Factor of 906,708,994 is 2

Step 1: Since 906 > 708, we apply the division lemma to 906 and 708, to get

906 = 708 x 1 + 198

Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 198 and 708, to get

708 = 198 x 3 + 114

Step 3: We consider the new divisor 198 and the new remainder 114, and apply the division lemma to get

198 = 114 x 1 + 84

We consider the new divisor 114 and the new remainder 84,and apply the division lemma to get

114 = 84 x 1 + 30

We consider the new divisor 84 and the new remainder 30,and apply the division lemma to get

84 = 30 x 2 + 24

We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get

30 = 24 x 1 + 6

We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get

24 = 6 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 906 and 708 is 6

Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(84,30) = HCF(114,84) = HCF(198,114) = HCF(708,198) = HCF(906,708) .

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

Step 1: Since 994 > 6, we apply the division lemma to 994 and 6, to get

994 = 6 x 165 + 4

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get

6 = 4 x 1 + 2

Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 994 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(994,6) .

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Frequently Asked Questions on HCF of 906, 708, 994 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 906, 708, 994?

Answer: HCF of 906, 708, 994 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 906, 708, 994 using Euclid's Algorithm?

Answer: For arbitrary numbers 906, 708, 994 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.