Highest Common Factor of 174, 243, 147 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 174, 243, 147 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 174, 243, 147 is 3 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 174, 243, 147 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 174, 243, 147 is 3.

HCF(174, 243, 147) = 3

HCF of 174, 243, 147 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 174, 243, 147 is 3.

Highest Common Factor of 174,243,147 using Euclid's algorithm

Highest Common Factor of 174,243,147 is 3

Step 1: Since 243 > 174, we apply the division lemma to 243 and 174, to get

243 = 174 x 1 + 69

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 69 and 174, to get

174 = 69 x 2 + 36

Step 3: We consider the new divisor 69 and the new remainder 36, and apply the division lemma to get

69 = 36 x 1 + 33

We consider the new divisor 36 and the new remainder 33,and apply the division lemma to get

36 = 33 x 1 + 3

We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get

33 = 3 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 174 and 243 is 3

Notice that 3 = HCF(33,3) = HCF(36,33) = HCF(69,36) = HCF(174,69) = HCF(243,174) .


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

Step 1: Since 147 > 3, we apply the division lemma to 147 and 3, to get

147 = 3 x 49 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 147 is 3

Notice that 3 = HCF(147,3) .

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Frequently Asked Questions on HCF of 174, 243, 147 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 174, 243, 147?

Answer: HCF of 174, 243, 147 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 174, 243, 147 using Euclid's Algorithm?

Answer: For arbitrary numbers 174, 243, 147 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.