Highest Common Factor of 770, 462, 457 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, 462, 457 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 770, 462, 457 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, 462, 457 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, 462, 457 is 1.

HCF(770, 462, 457) = 1

HCF of 770, 462, 457 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, 462, 457 is 1.

Highest Common Factor of 770,462,457 using Euclid's algorithm

Highest Common Factor of 770,462,457 is 1

Step 1: Since 770 > 462, we apply the division lemma to 770 and 462, to get

770 = 462 x 1 + 308

Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 308 and 462, to get

462 = 308 x 1 + 154

Step 3: We consider the new divisor 308 and the new remainder 154, and apply the division lemma to get

308 = 154 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 154, the HCF of 770 and 462 is 154

Notice that 154 = HCF(308,154) = HCF(462,308) = HCF(770,462) .

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

Step 1: Since 457 > 154, we apply the division lemma to 457 and 154, to get

457 = 154 x 2 + 149

Step 2: Since the reminder 154 ≠ 0, we apply division lemma to 149 and 154, to get

154 = 149 x 1 + 5

Step 3: We consider the new divisor 149 and the new remainder 5, and apply the division lemma to get

149 = 5 x 29 + 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 154 and 457 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(149,5) = HCF(154,149) = HCF(457,154) .

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Frequently Asked Questions on HCF of 770, 462, 457 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, 462, 457?

Answer: HCF of 770, 462, 457 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 770, 462, 457 using Euclid's Algorithm?

Answer: For arbitrary numbers 770, 462, 457 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.