Highest Common Factor of 505, 800, 736 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, 800, 736 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 800, 736 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, 800, 736 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, 800, 736 is 1.

HCF(505, 800, 736) = 1

HCF of 505, 800, 736 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, 800, 736 is 1.

Highest Common Factor of 505,800,736 using Euclid's algorithm

Highest Common Factor of 505,800,736 is 1

Step 1: Since 800 > 505, we apply the division lemma to 800 and 505, to get

800 = 505 x 1 + 295

Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 295 and 505, to get

505 = 295 x 1 + 210

Step 3: We consider the new divisor 295 and the new remainder 210, and apply the division lemma to get

295 = 210 x 1 + 85

We consider the new divisor 210 and the new remainder 85,and apply the division lemma to get

210 = 85 x 2 + 40

We consider the new divisor 85 and the new remainder 40,and apply the division lemma to get

85 = 40 x 2 + 5

We consider the new divisor 40 and the new remainder 5,and apply the division lemma to get

40 = 5 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 505 and 800 is 5

Notice that 5 = HCF(40,5) = HCF(85,40) = HCF(210,85) = HCF(295,210) = HCF(505,295) = HCF(800,505) .

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

Step 1: Since 736 > 5, we apply the division lemma to 736 and 5, to get

736 = 5 x 147 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 736 is 1

Notice that 1 = HCF(5,1) = HCF(736,5) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 505, 800, 736 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, 800, 736?

Answer: HCF of 505, 800, 736 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 800, 736 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 800, 736 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.