Highest Common Factor of 473, 661, 354 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 473, 661, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 473, 661, 354 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 473, 661, 354 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 473, 661, 354 is 1.

HCF(473, 661, 354) = 1

HCF of 473, 661, 354 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 473, 661, 354 is 1.

Highest Common Factor of 473,661,354 using Euclid's algorithm

Highest Common Factor of 473,661,354 is 1

Step 1: Since 661 > 473, we apply the division lemma to 661 and 473, to get

661 = 473 x 1 + 188

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 188 and 473, to get

473 = 188 x 2 + 97

Step 3: We consider the new divisor 188 and the new remainder 97, and apply the division lemma to get

188 = 97 x 1 + 91

We consider the new divisor 97 and the new remainder 91,and apply the division lemma to get

97 = 91 x 1 + 6

We consider the new divisor 91 and the new remainder 6,and apply the division lemma to get

91 = 6 x 15 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 473 and 661 is 1

Notice that 1 = HCF(6,1) = HCF(91,6) = HCF(97,91) = HCF(188,97) = HCF(473,188) = HCF(661,473) .

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

Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get

354 = 1 x 354 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1

Notice that 1 = HCF(354,1) .

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Frequently Asked Questions on HCF of 473, 661, 354 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 473, 661, 354?

Answer: HCF of 473, 661, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 473, 661, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 473, 661, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.