Highest Common Factor of 473, 770, 910, 474 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 473, 770, 910, 474 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 473, 770, 910, 474 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 473, 770, 910, 474 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 473, 770, 910, 474 is 1.

HCF(473, 770, 910, 474) = 1

HCF of 473, 770, 910, 474 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 473, 770, 910, 474 is 1.

Highest Common Factor of 473,770,910,474 using Euclid's algorithm

Highest Common Factor of 473,770,910,474 is 1

Step 1: Since 770 > 473, we apply the division lemma to 770 and 473, to get

770 = 473 x 1 + 297

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 297 and 473, to get

473 = 297 x 1 + 176

Step 3: We consider the new divisor 297 and the new remainder 176, and apply the division lemma to get

297 = 176 x 1 + 121

We consider the new divisor 176 and the new remainder 121,and apply the division lemma to get

176 = 121 x 1 + 55

We consider the new divisor 121 and the new remainder 55,and apply the division lemma to get

121 = 55 x 2 + 11

We consider the new divisor 55 and the new remainder 11,and apply the division lemma to get

55 = 11 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 473 and 770 is 11

Notice that 11 = HCF(55,11) = HCF(121,55) = HCF(176,121) = HCF(297,176) = HCF(473,297) = HCF(770,473) .

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

Step 1: Since 910 > 11, we apply the division lemma to 910 and 11, to get

910 = 11 x 82 + 8

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 8 and 11, to get

11 = 8 x 1 + 3

Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 11 and 910 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(910,11) .

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

Step 1: Since 474 > 1, we apply the division lemma to 474 and 1, to get

474 = 1 x 474 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 474 is 1

Notice that 1 = HCF(474,1) .

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Frequently Asked Questions on HCF of 473, 770, 910, 474 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 473, 770, 910, 474?

Answer: HCF of 473, 770, 910, 474 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 473, 770, 910, 474 using Euclid's Algorithm?

Answer: For arbitrary numbers 473, 770, 910, 474 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.