Highest Common Factor of 845, 990, 966 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 845, 990, 966 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 845, 990, 966 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 845, 990, 966 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 845, 990, 966 is 1.

HCF(845, 990, 966) = 1

HCF of 845, 990, 966 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 845, 990, 966 is 1.

Highest Common Factor of 845,990,966 using Euclid's algorithm

Highest Common Factor of 845,990,966 is 1

Step 1: Since 990 > 845, we apply the division lemma to 990 and 845, to get

990 = 845 x 1 + 145

Step 2: Since the reminder 845 ≠ 0, we apply division lemma to 145 and 845, to get

845 = 145 x 5 + 120

Step 3: We consider the new divisor 145 and the new remainder 120, and apply the division lemma to get

145 = 120 x 1 + 25

We consider the new divisor 120 and the new remainder 25,and apply the division lemma to get

120 = 25 x 4 + 20

We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get

25 = 20 x 1 + 5

We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 845 and 990 is 5

Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(120,25) = HCF(145,120) = HCF(845,145) = HCF(990,845) .

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

Step 1: Since 966 > 5, we apply the division lemma to 966 and 5, to get

966 = 5 x 193 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, 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 5 and 966 is 1

Notice that 1 = HCF(5,1) = HCF(966,5) .

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Frequently Asked Questions on HCF of 845, 990, 966 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 845, 990, 966?

Answer: HCF of 845, 990, 966 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 845, 990, 966 using Euclid's Algorithm?

Answer: For arbitrary numbers 845, 990, 966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.