Highest Common Factor of 505, 1197, 1746 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 505, 1197, 1746 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 1197, 1746 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 505, 1197, 1746 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 505, 1197, 1746 is 1.

HCF(505, 1197, 1746) = 1

HCF of 505, 1197, 1746 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 505, 1197, 1746 is 1.

Highest Common Factor of 505,1197,1746 using Euclid's algorithm

Highest Common Factor of 505,1197,1746 is 1

Step 1: Since 1197 > 505, we apply the division lemma to 1197 and 505, to get

1197 = 505 x 2 + 187

Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 187 and 505, to get

505 = 187 x 2 + 131

Step 3: We consider the new divisor 187 and the new remainder 131, and apply the division lemma to get

187 = 131 x 1 + 56

We consider the new divisor 131 and the new remainder 56,and apply the division lemma to get

131 = 56 x 2 + 19

We consider the new divisor 56 and the new remainder 19,and apply the division lemma to get

56 = 19 x 2 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 505 and 1197 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(56,19) = HCF(131,56) = HCF(187,131) = HCF(505,187) = HCF(1197,505) .

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

Step 1: Since 1746 > 1, we apply the division lemma to 1746 and 1, to get

1746 = 1 x 1746 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1746 is 1

Notice that 1 = HCF(1746,1) .

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Frequently Asked Questions on HCF of 505, 1197, 1746 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 505, 1197, 1746?

Answer: HCF of 505, 1197, 1746 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 1197, 1746 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 1197, 1746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.