Highest Common Factor of 364, 473, 162 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 364, 473, 162 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 364, 473, 162 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 364, 473, 162 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 364, 473, 162 is 1.

HCF(364, 473, 162) = 1

HCF of 364, 473, 162 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 364, 473, 162 is 1.

Highest Common Factor of 364,473,162 using Euclid's algorithm

Highest Common Factor of 364,473,162 is 1

Step 1: Since 473 > 364, we apply the division lemma to 473 and 364, to get

473 = 364 x 1 + 109

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 109 and 364, to get

364 = 109 x 3 + 37

Step 3: We consider the new divisor 109 and the new remainder 37, and apply the division lemma to get

109 = 37 x 2 + 35

We consider the new divisor 37 and the new remainder 35,and apply the division lemma to get

37 = 35 x 1 + 2

We consider the new divisor 35 and the new remainder 2,and apply the division lemma to get

35 = 2 x 17 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 364 and 473 is 1

Notice that 1 = HCF(2,1) = HCF(35,2) = HCF(37,35) = HCF(109,37) = HCF(364,109) = HCF(473,364) .

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

Step 1: Since 162 > 1, we apply the division lemma to 162 and 1, to get

162 = 1 x 162 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 162 is 1

Notice that 1 = HCF(162,1) .

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Frequently Asked Questions on HCF of 364, 473, 162 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 364, 473, 162?

Answer: HCF of 364, 473, 162 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 364, 473, 162 using Euclid's Algorithm?

Answer: For arbitrary numbers 364, 473, 162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.