Highest Common Factor of 824, 233, 160 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 824, 233, 160 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 824, 233, 160 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 824, 233, 160 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 824, 233, 160 is 1.

HCF(824, 233, 160) = 1

HCF of 824, 233, 160 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 824, 233, 160 is 1.

Highest Common Factor of 824,233,160 using Euclid's algorithm

Highest Common Factor of 824,233,160 is 1

Step 1: Since 824 > 233, we apply the division lemma to 824 and 233, to get

824 = 233 x 3 + 125

Step 2: Since the reminder 233 ≠ 0, we apply division lemma to 125 and 233, to get

233 = 125 x 1 + 108

Step 3: We consider the new divisor 125 and the new remainder 108, and apply the division lemma to get

125 = 108 x 1 + 17

We consider the new divisor 108 and the new remainder 17,and apply the division lemma to get

108 = 17 x 6 + 6

We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get

17 = 6 x 2 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

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 824 and 233 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(108,17) = HCF(125,108) = HCF(233,125) = HCF(824,233) .

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

Step 1: Since 160 > 1, we apply the division lemma to 160 and 1, to get

160 = 1 x 160 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 160 is 1

Notice that 1 = HCF(160,1) .

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Frequently Asked Questions on HCF of 824, 233, 160 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 824, 233, 160?

Answer: HCF of 824, 233, 160 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 824, 233, 160 using Euclid's Algorithm?

Answer: For arbitrary numbers 824, 233, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.