Highest Common Factor of 477, 734, 705 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 477, 734, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 477, 734, 705 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 477, 734, 705 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 477, 734, 705 is 1.

HCF(477, 734, 705) = 1

HCF of 477, 734, 705 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 477, 734, 705 is 1.

Highest Common Factor of 477,734,705 using Euclid's algorithm

Highest Common Factor of 477,734,705 is 1

Step 1: Since 734 > 477, we apply the division lemma to 734 and 477, to get

734 = 477 x 1 + 257

Step 2: Since the reminder 477 ≠ 0, we apply division lemma to 257 and 477, to get

477 = 257 x 1 + 220

Step 3: We consider the new divisor 257 and the new remainder 220, and apply the division lemma to get

257 = 220 x 1 + 37

We consider the new divisor 220 and the new remainder 37,and apply the division lemma to get

220 = 37 x 5 + 35

We consider the new divisor 37 and the new remainder 35,and apply the division lemma to get

37 = 35 x 1 + 2

We consider the new divisor 35 and the new remainder 2,and apply the division lemma to get

35 = 2 x 17 + 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 477 and 734 is 1

Notice that 1 = HCF(2,1) = HCF(35,2) = HCF(37,35) = HCF(220,37) = HCF(257,220) = HCF(477,257) = HCF(734,477) .

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

Step 1: Since 705 > 1, we apply the division lemma to 705 and 1, to get

705 = 1 x 705 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 705 is 1

Notice that 1 = HCF(705,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 477, 734, 705 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 477, 734, 705?

Answer: HCF of 477, 734, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 477, 734, 705 using Euclid's Algorithm?

Answer: For arbitrary numbers 477, 734, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.