Highest Common Factor of 770, 470, 493 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 770, 470, 493 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 770, 470, 493 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 770, 470, 493 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 770, 470, 493 is 1.

HCF(770, 470, 493) = 1

HCF of 770, 470, 493 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 770, 470, 493 is 1.

Highest Common Factor of 770,470,493 using Euclid's algorithm

Highest Common Factor of 770,470,493 is 1

Step 1: Since 770 > 470, we apply the division lemma to 770 and 470, to get

770 = 470 x 1 + 300

Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 300 and 470, to get

470 = 300 x 1 + 170

Step 3: We consider the new divisor 300 and the new remainder 170, and apply the division lemma to get

300 = 170 x 1 + 130

We consider the new divisor 170 and the new remainder 130,and apply the division lemma to get

170 = 130 x 1 + 40

We consider the new divisor 130 and the new remainder 40,and apply the division lemma to get

130 = 40 x 3 + 10

We consider the new divisor 40 and the new remainder 10,and apply the division lemma to get

40 = 10 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 770 and 470 is 10

Notice that 10 = HCF(40,10) = HCF(130,40) = HCF(170,130) = HCF(300,170) = HCF(470,300) = HCF(770,470) .

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

Step 1: Since 493 > 10, we apply the division lemma to 493 and 10, to get

493 = 10 x 49 + 3

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 3 and 10, to get

10 = 3 x 3 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 493 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(493,10) .

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Frequently Asked Questions on HCF of 770, 470, 493 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 770, 470, 493?

Answer: HCF of 770, 470, 493 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 770, 470, 493 using Euclid's Algorithm?

Answer: For arbitrary numbers 770, 470, 493 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.