Highest Common Factor of 345, 869, 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 345, 869, 160 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 345, 869, 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 345, 869, 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 345, 869, 160 is 1.

HCF(345, 869, 160) = 1

HCF of 345, 869, 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 345, 869, 160 is 1.

Highest Common Factor of 345,869,160 using Euclid's algorithm

Highest Common Factor of 345,869,160 is 1

Step 1: Since 869 > 345, we apply the division lemma to 869 and 345, to get

869 = 345 x 2 + 179

Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 179 and 345, to get

345 = 179 x 1 + 166

Step 3: We consider the new divisor 179 and the new remainder 166, and apply the division lemma to get

179 = 166 x 1 + 13

We consider the new divisor 166 and the new remainder 13,and apply the division lemma to get

166 = 13 x 12 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 345 and 869 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(166,13) = HCF(179,166) = HCF(345,179) = HCF(869,345) .

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 345, 869, 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 345, 869, 160?

Answer: HCF of 345, 869, 160 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 345, 869, 160 using Euclid's Algorithm?

Answer: For arbitrary numbers 345, 869, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.