Highest Common Factor of 450, 996, 161 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 450, 996, 161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 450, 996, 161 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 450, 996, 161 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 450, 996, 161 is 1.

HCF(450, 996, 161) = 1

HCF of 450, 996, 161 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 450, 996, 161 is 1.

Highest Common Factor of 450,996,161 using Euclid's algorithm

Highest Common Factor of 450,996,161 is 1

Step 1: Since 996 > 450, we apply the division lemma to 996 and 450, to get

996 = 450 x 2 + 96

Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 96 and 450, to get

450 = 96 x 4 + 66

Step 3: We consider the new divisor 96 and the new remainder 66, and apply the division lemma to get

96 = 66 x 1 + 30

We consider the new divisor 66 and the new remainder 30,and apply the division lemma to get

66 = 30 x 2 + 6

We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get

30 = 6 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 450 and 996 is 6

Notice that 6 = HCF(30,6) = HCF(66,30) = HCF(96,66) = HCF(450,96) = HCF(996,450) .

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

Step 1: Since 161 > 6, we apply the division lemma to 161 and 6, to get

161 = 6 x 26 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma 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 6 and 161 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(161,6) .

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Frequently Asked Questions on HCF of 450, 996, 161 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 450, 996, 161?

Answer: HCF of 450, 996, 161 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 450, 996, 161 using Euclid's Algorithm?

Answer: For arbitrary numbers 450, 996, 161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.