Highest Common Factor of 505, 320, 762 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, 320, 762 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 320, 762 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, 320, 762 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, 320, 762 is 1.

HCF(505, 320, 762) = 1

HCF of 505, 320, 762 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, 320, 762 is 1.

Highest Common Factor of 505,320,762 using Euclid's algorithm

Highest Common Factor of 505,320,762 is 1

Step 1: Since 505 > 320, we apply the division lemma to 505 and 320, to get

505 = 320 x 1 + 185

Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 185 and 320, to get

320 = 185 x 1 + 135

Step 3: We consider the new divisor 185 and the new remainder 135, and apply the division lemma to get

185 = 135 x 1 + 50

We consider the new divisor 135 and the new remainder 50,and apply the division lemma to get

135 = 50 x 2 + 35

We consider the new divisor 50 and the new remainder 35,and apply the division lemma to get

50 = 35 x 1 + 15

We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get

35 = 15 x 2 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 505 and 320 is 5

Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(50,35) = HCF(135,50) = HCF(185,135) = HCF(320,185) = HCF(505,320) .

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

Step 1: Since 762 > 5, we apply the division lemma to 762 and 5, to get

762 = 5 x 152 + 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 762 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(762,5) .

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Frequently Asked Questions on HCF of 505, 320, 762 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, 320, 762?

Answer: HCF of 505, 320, 762 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 320, 762 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 320, 762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.