Highest Common Factor of 648, 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 648, 473 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 648, 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 648, 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 648, 473 is 1.

HCF(648, 473) = 1

HCF of 648, 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 648, 473 is 1.

Highest Common Factor of 648,473 using Euclid's algorithm

Highest Common Factor of 648,473 is 1

Step 1: Since 648 > 473, we apply the division lemma to 648 and 473, to get

648 = 473 x 1 + 175

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 175 and 473, to get

473 = 175 x 2 + 123

Step 3: We consider the new divisor 175 and the new remainder 123, and apply the division lemma to get

175 = 123 x 1 + 52

We consider the new divisor 123 and the new remainder 52,and apply the division lemma to get

123 = 52 x 2 + 19

We consider the new divisor 52 and the new remainder 19,and apply the division lemma to get

52 = 19 x 2 + 14

We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 648 and 473 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(52,19) = HCF(123,52) = HCF(175,123) = HCF(473,175) = HCF(648,473) .

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Frequently Asked Questions on HCF of 648, 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 648, 473?

Answer: HCF of 648, 473 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 648, 473 using Euclid's Algorithm?

Answer: For arbitrary numbers 648, 473 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.