Highest Common Factor of 661, 403, 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 661, 403, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 661, 403, 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 661, 403, 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 661, 403, 705 is 1.

HCF(661, 403, 705) = 1

HCF of 661, 403, 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 661, 403, 705 is 1.

Highest Common Factor of 661,403,705 using Euclid's algorithm

Highest Common Factor of 661,403,705 is 1

Step 1: Since 661 > 403, we apply the division lemma to 661 and 403, to get

661 = 403 x 1 + 258

Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 258 and 403, to get

403 = 258 x 1 + 145

Step 3: We consider the new divisor 258 and the new remainder 145, and apply the division lemma to get

258 = 145 x 1 + 113

We consider the new divisor 145 and the new remainder 113,and apply the division lemma to get

145 = 113 x 1 + 32

We consider the new divisor 113 and the new remainder 32,and apply the division lemma to get

113 = 32 x 3 + 17

We consider the new divisor 32 and the new remainder 17,and apply the division lemma to get

32 = 17 x 1 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 661 and 403 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(32,17) = HCF(113,32) = HCF(145,113) = HCF(258,145) = HCF(403,258) = HCF(661,403) .

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) .

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Frequently Asked Questions on HCF of 661, 403, 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 661, 403, 705?

Answer: HCF of 661, 403, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 661, 403, 705 using Euclid's Algorithm?

Answer: For arbitrary numbers 661, 403, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.