Highest Common Factor of 703, 435, 178 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 703, 435, 178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 703, 435, 178 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 703, 435, 178 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 703, 435, 178 is 1.

HCF(703, 435, 178) = 1

HCF of 703, 435, 178 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 703, 435, 178 is 1.

Highest Common Factor of 703,435,178 using Euclid's algorithm

Highest Common Factor of 703,435,178 is 1

Step 1: Since 703 > 435, we apply the division lemma to 703 and 435, to get

703 = 435 x 1 + 268

Step 2: Since the reminder 435 ≠ 0, we apply division lemma to 268 and 435, to get

435 = 268 x 1 + 167

Step 3: We consider the new divisor 268 and the new remainder 167, and apply the division lemma to get

268 = 167 x 1 + 101

We consider the new divisor 167 and the new remainder 101,and apply the division lemma to get

167 = 101 x 1 + 66

We consider the new divisor 101 and the new remainder 66,and apply the division lemma to get

101 = 66 x 1 + 35

We consider the new divisor 66 and the new remainder 35,and apply the division lemma to get

66 = 35 x 1 + 31

We consider the new divisor 35 and the new remainder 31,and apply the division lemma to get

35 = 31 x 1 + 4

We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get

31 = 4 x 7 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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 703 and 435 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(35,31) = HCF(66,35) = HCF(101,66) = HCF(167,101) = HCF(268,167) = HCF(435,268) = HCF(703,435) .

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

Step 1: Since 178 > 1, we apply the division lemma to 178 and 1, to get

178 = 1 x 178 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 178 is 1

Notice that 1 = HCF(178,1) .

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Frequently Asked Questions on HCF of 703, 435, 178 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 703, 435, 178?

Answer: HCF of 703, 435, 178 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 703, 435, 178 using Euclid's Algorithm?

Answer: For arbitrary numbers 703, 435, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.