Highest Common Factor of 992, 410, 145 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 992, 410, 145 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 992, 410, 145 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 992, 410, 145 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 992, 410, 145 is 1.

HCF(992, 410, 145) = 1

HCF of 992, 410, 145 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 992, 410, 145 is 1.

Highest Common Factor of 992,410,145 using Euclid's algorithm

Highest Common Factor of 992,410,145 is 1

Step 1: Since 992 > 410, we apply the division lemma to 992 and 410, to get

992 = 410 x 2 + 172

Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 172 and 410, to get

410 = 172 x 2 + 66

Step 3: We consider the new divisor 172 and the new remainder 66, and apply the division lemma to get

172 = 66 x 2 + 40

We consider the new divisor 66 and the new remainder 40,and apply the division lemma to get

66 = 40 x 1 + 26

We consider the new divisor 40 and the new remainder 26,and apply the division lemma to get

40 = 26 x 1 + 14

We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 992 and 410 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(66,40) = HCF(172,66) = HCF(410,172) = HCF(992,410) .

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

Step 1: Since 145 > 2, we apply the division lemma to 145 and 2, to get

145 = 2 x 72 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 145 is 1

Notice that 1 = HCF(2,1) = HCF(145,2) .

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Frequently Asked Questions on HCF of 992, 410, 145 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 992, 410, 145?

Answer: HCF of 992, 410, 145 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 992, 410, 145 using Euclid's Algorithm?

Answer: For arbitrary numbers 992, 410, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.