Highest Common Factor of 470, 722, 849 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 470, 722, 849 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 470, 722, 849 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 470, 722, 849 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 470, 722, 849 is 1.

HCF(470, 722, 849) = 1

HCF of 470, 722, 849 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 470, 722, 849 is 1.

Highest Common Factor of 470,722,849 using Euclid's algorithm

Highest Common Factor of 470,722,849 is 1

Step 1: Since 722 > 470, we apply the division lemma to 722 and 470, to get

722 = 470 x 1 + 252

Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 252 and 470, to get

470 = 252 x 1 + 218

Step 3: We consider the new divisor 252 and the new remainder 218, and apply the division lemma to get

252 = 218 x 1 + 34

We consider the new divisor 218 and the new remainder 34,and apply the division lemma to get

218 = 34 x 6 + 14

We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get

34 = 14 x 2 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 470 and 722 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(218,34) = HCF(252,218) = HCF(470,252) = HCF(722,470) .

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

Step 1: Since 849 > 2, we apply the division lemma to 849 and 2, to get

849 = 2 x 424 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 849 is 1

Notice that 1 = HCF(2,1) = HCF(849,2) .

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Frequently Asked Questions on HCF of 470, 722, 849 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 470, 722, 849?

Answer: HCF of 470, 722, 849 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 470, 722, 849 using Euclid's Algorithm?

Answer: For arbitrary numbers 470, 722, 849 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.