Highest Common Factor of 446, 723, 986 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 446, 723, 986 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 446, 723, 986 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 446, 723, 986 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 446, 723, 986 is 1.

HCF(446, 723, 986) = 1

HCF of 446, 723, 986 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 446, 723, 986 is 1.

Highest Common Factor of 446,723,986 using Euclid's algorithm

Highest Common Factor of 446,723,986 is 1

Step 1: Since 723 > 446, we apply the division lemma to 723 and 446, to get

723 = 446 x 1 + 277

Step 2: Since the reminder 446 ≠ 0, we apply division lemma to 277 and 446, to get

446 = 277 x 1 + 169

Step 3: We consider the new divisor 277 and the new remainder 169, and apply the division lemma to get

277 = 169 x 1 + 108

We consider the new divisor 169 and the new remainder 108,and apply the division lemma to get

169 = 108 x 1 + 61

We consider the new divisor 108 and the new remainder 61,and apply the division lemma to get

108 = 61 x 1 + 47

We consider the new divisor 61 and the new remainder 47,and apply the division lemma to get

61 = 47 x 1 + 14

We consider the new divisor 47 and the new remainder 14,and apply the division lemma to get

47 = 14 x 3 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 446 and 723 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(47,14) = HCF(61,47) = HCF(108,61) = HCF(169,108) = HCF(277,169) = HCF(446,277) = HCF(723,446) .

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

Step 1: Since 986 > 1, we apply the division lemma to 986 and 1, to get

986 = 1 x 986 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 986 is 1

Notice that 1 = HCF(986,1) .

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Frequently Asked Questions on HCF of 446, 723, 986 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 446, 723, 986?

Answer: HCF of 446, 723, 986 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 446, 723, 986 using Euclid's Algorithm?

Answer: For arbitrary numbers 446, 723, 986 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.