Highest Common Factor of 685, 505, 757 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 685, 505, 757 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 505, 757 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 685, 505, 757 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 685, 505, 757 is 1.

HCF(685, 505, 757) = 1

HCF of 685, 505, 757 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 685, 505, 757 is 1.

Highest Common Factor of 685,505,757 using Euclid's algorithm

Highest Common Factor of 685,505,757 is 1

Step 1: Since 685 > 505, we apply the division lemma to 685 and 505, to get

685 = 505 x 1 + 180

Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 180 and 505, to get

505 = 180 x 2 + 145

Step 3: We consider the new divisor 180 and the new remainder 145, and apply the division lemma to get

180 = 145 x 1 + 35

We consider the new divisor 145 and the new remainder 35,and apply the division lemma to get

145 = 35 x 4 + 5

We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get

35 = 5 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 685 and 505 is 5

Notice that 5 = HCF(35,5) = HCF(145,35) = HCF(180,145) = HCF(505,180) = HCF(685,505) .

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

Step 1: Since 757 > 5, we apply the division lemma to 757 and 5, to get

757 = 5 x 151 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 1

Step 3: 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 5 and 757 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(757,5) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 685, 505, 757 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 685, 505, 757?

Answer: HCF of 685, 505, 757 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 505, 757 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 505, 757 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.