Highest Common Factor of 703, 1603, 8516 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, 1603, 8516 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 703, 1603, 8516 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, 1603, 8516 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, 1603, 8516 is 1.

HCF(703, 1603, 8516) = 1

HCF of 703, 1603, 8516 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, 1603, 8516 is 1.

Highest Common Factor of 703,1603,8516 using Euclid's algorithm

Highest Common Factor of 703,1603,8516 is 1

Step 1: Since 1603 > 703, we apply the division lemma to 1603 and 703, to get

1603 = 703 x 2 + 197

Step 2: Since the reminder 703 ≠ 0, we apply division lemma to 197 and 703, to get

703 = 197 x 3 + 112

Step 3: We consider the new divisor 197 and the new remainder 112, and apply the division lemma to get

197 = 112 x 1 + 85

We consider the new divisor 112 and the new remainder 85,and apply the division lemma to get

112 = 85 x 1 + 27

We consider the new divisor 85 and the new remainder 27,and apply the division lemma to get

85 = 27 x 3 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 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 1603 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(85,27) = HCF(112,85) = HCF(197,112) = HCF(703,197) = HCF(1603,703) .

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

Step 1: Since 8516 > 1, we apply the division lemma to 8516 and 1, to get

8516 = 1 x 8516 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8516 is 1

Notice that 1 = HCF(8516,1) .

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Frequently Asked Questions on HCF of 703, 1603, 8516 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, 1603, 8516?

Answer: HCF of 703, 1603, 8516 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 703, 1603, 8516 using Euclid's Algorithm?

Answer: For arbitrary numbers 703, 1603, 8516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.