Highest Common Factor of 465, 721, 223 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 465, 721, 223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 465, 721, 223 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 465, 721, 223 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 465, 721, 223 is 1.

HCF(465, 721, 223) = 1

HCF of 465, 721, 223 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 465, 721, 223 is 1.

Highest Common Factor of 465,721,223 using Euclid's algorithm

Highest Common Factor of 465,721,223 is 1

Step 1: Since 721 > 465, we apply the division lemma to 721 and 465, to get

721 = 465 x 1 + 256

Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 256 and 465, to get

465 = 256 x 1 + 209

Step 3: We consider the new divisor 256 and the new remainder 209, and apply the division lemma to get

256 = 209 x 1 + 47

We consider the new divisor 209 and the new remainder 47,and apply the division lemma to get

209 = 47 x 4 + 21

We consider the new divisor 47 and the new remainder 21,and apply the division lemma to get

47 = 21 x 2 + 5

We consider the new divisor 21 and the new remainder 5,and apply the division lemma to get

21 = 5 x 4 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 465 and 721 is 1

Notice that 1 = HCF(5,1) = HCF(21,5) = HCF(47,21) = HCF(209,47) = HCF(256,209) = HCF(465,256) = HCF(721,465) .

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

Step 1: Since 223 > 1, we apply the division lemma to 223 and 1, to get

223 = 1 x 223 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 223 is 1

Notice that 1 = HCF(223,1) .

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Frequently Asked Questions on HCF of 465, 721, 223 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 465, 721, 223?

Answer: HCF of 465, 721, 223 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 465, 721, 223 using Euclid's Algorithm?

Answer: For arbitrary numbers 465, 721, 223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.