Highest Common Factor of 374, 615, 473 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 374, 615, 473 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 374, 615, 473 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 374, 615, 473 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 374, 615, 473 is 1.

HCF(374, 615, 473) = 1

HCF of 374, 615, 473 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 374, 615, 473 is 1.

Highest Common Factor of 374,615,473 using Euclid's algorithm

Highest Common Factor of 374,615,473 is 1

Step 1: Since 615 > 374, we apply the division lemma to 615 and 374, to get

615 = 374 x 1 + 241

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 241 and 374, to get

374 = 241 x 1 + 133

Step 3: We consider the new divisor 241 and the new remainder 133, and apply the division lemma to get

241 = 133 x 1 + 108

We consider the new divisor 133 and the new remainder 108,and apply the division lemma to get

133 = 108 x 1 + 25

We consider the new divisor 108 and the new remainder 25,and apply the division lemma to get

108 = 25 x 4 + 8

We consider the new divisor 25 and the new remainder 8,and apply the division lemma to get

25 = 8 x 3 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 374 and 615 is 1

Notice that 1 = HCF(8,1) = HCF(25,8) = HCF(108,25) = HCF(133,108) = HCF(241,133) = HCF(374,241) = HCF(615,374) .

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

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

473 = 1 x 473 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 473 is 1

Notice that 1 = HCF(473,1) .

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Frequently Asked Questions on HCF of 374, 615, 473 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 374, 615, 473?

Answer: HCF of 374, 615, 473 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 374, 615, 473 using Euclid's Algorithm?

Answer: For arbitrary numbers 374, 615, 473 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.