Highest Common Factor of 507, 780, 83 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 507, 780, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 507, 780, 83 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 507, 780, 83 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 507, 780, 83 is 1.

HCF(507, 780, 83) = 1

HCF of 507, 780, 83 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 507, 780, 83 is 1.

Highest Common Factor of 507,780,83 using Euclid's algorithm

Highest Common Factor of 507,780,83 is 1

Step 1: Since 780 > 507, we apply the division lemma to 780 and 507, to get

780 = 507 x 1 + 273

Step 2: Since the reminder 507 ≠ 0, we apply division lemma to 273 and 507, to get

507 = 273 x 1 + 234

Step 3: We consider the new divisor 273 and the new remainder 234, and apply the division lemma to get

273 = 234 x 1 + 39

We consider the new divisor 234 and the new remainder 39, and apply the division lemma to get

234 = 39 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 507 and 780 is 39

Notice that 39 = HCF(234,39) = HCF(273,234) = HCF(507,273) = HCF(780,507) .

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

Step 1: Since 83 > 39, we apply the division lemma to 83 and 39, to get

83 = 39 x 2 + 5

Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 5 and 39, to get

39 = 5 x 7 + 4

Step 3: We consider the new divisor 5 and the new remainder 4, and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 39 and 83 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(39,5) = HCF(83,39) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 507, 780, 83 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 507, 780, 83?

Answer: HCF of 507, 780, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 507, 780, 83 using Euclid's Algorithm?

Answer: For arbitrary numbers 507, 780, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.