Highest Common Factor of 103, 465, 692 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 103, 465, 692 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 103, 465, 692 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 103, 465, 692 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 103, 465, 692 is 1.

HCF(103, 465, 692) = 1

HCF of 103, 465, 692 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 103, 465, 692 is 1.

Highest Common Factor of 103,465,692 using Euclid's algorithm

Highest Common Factor of 103,465,692 is 1

Step 1: Since 465 > 103, we apply the division lemma to 465 and 103, to get

465 = 103 x 4 + 53

Step 2: Since the reminder 103 ≠ 0, we apply division lemma to 53 and 103, to get

103 = 53 x 1 + 50

Step 3: We consider the new divisor 53 and the new remainder 50, and apply the division lemma to get

53 = 50 x 1 + 3

We consider the new divisor 50 and the new remainder 3,and apply the division lemma to get

50 = 3 x 16 + 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 103 and 465 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(50,3) = HCF(53,50) = HCF(103,53) = HCF(465,103) .

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

Step 1: Since 692 > 1, we apply the division lemma to 692 and 1, to get

692 = 1 x 692 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 692 is 1

Notice that 1 = HCF(692,1) .

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Frequently Asked Questions on HCF of 103, 465, 692 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 103, 465, 692?

Answer: HCF of 103, 465, 692 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 103, 465, 692 using Euclid's Algorithm?

Answer: For arbitrary numbers 103, 465, 692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.