Highest Common Factor of 523, 921, 780 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 523, 921, 780 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 921, 780 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 523, 921, 780 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 523, 921, 780 is 1.

HCF(523, 921, 780) = 1

HCF of 523, 921, 780 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 523, 921, 780 is 1.

Highest Common Factor of 523,921,780 using Euclid's algorithm

Highest Common Factor of 523,921,780 is 1

Step 1: Since 921 > 523, we apply the division lemma to 921 and 523, to get

921 = 523 x 1 + 398

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 398 and 523, to get

523 = 398 x 1 + 125

Step 3: We consider the new divisor 398 and the new remainder 125, and apply the division lemma to get

398 = 125 x 3 + 23

We consider the new divisor 125 and the new remainder 23,and apply the division lemma to get

125 = 23 x 5 + 10

We consider the new divisor 23 and the new remainder 10,and apply the division lemma to get

23 = 10 x 2 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 523 and 921 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(23,10) = HCF(125,23) = HCF(398,125) = HCF(523,398) = HCF(921,523) .

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

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

780 = 1 x 780 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 780 is 1

Notice that 1 = HCF(780,1) .

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Frequently Asked Questions on HCF of 523, 921, 780 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 523, 921, 780?

Answer: HCF of 523, 921, 780 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 921, 780 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 921, 780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.