Highest Common Factor of 786, 480, 713 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 786, 480, 713 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 786, 480, 713 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 786, 480, 713 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 786, 480, 713 is 1.

HCF(786, 480, 713) = 1

HCF of 786, 480, 713 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 786, 480, 713 is 1.

Highest Common Factor of 786,480,713 using Euclid's algorithm

Highest Common Factor of 786,480,713 is 1

Step 1: Since 786 > 480, we apply the division lemma to 786 and 480, to get

786 = 480 x 1 + 306

Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 306 and 480, to get

480 = 306 x 1 + 174

Step 3: We consider the new divisor 306 and the new remainder 174, and apply the division lemma to get

306 = 174 x 1 + 132

We consider the new divisor 174 and the new remainder 132,and apply the division lemma to get

174 = 132 x 1 + 42

We consider the new divisor 132 and the new remainder 42,and apply the division lemma to get

132 = 42 x 3 + 6

We consider the new divisor 42 and the new remainder 6,and apply the division lemma to get

42 = 6 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 786 and 480 is 6

Notice that 6 = HCF(42,6) = HCF(132,42) = HCF(174,132) = HCF(306,174) = HCF(480,306) = HCF(786,480) .

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

Step 1: Since 713 > 6, we apply the division lemma to 713 and 6, to get

713 = 6 x 118 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma 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 6 and 713 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(713,6) .

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Frequently Asked Questions on HCF of 786, 480, 713 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 786, 480, 713?

Answer: HCF of 786, 480, 713 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 786, 480, 713 using Euclid's Algorithm?

Answer: For arbitrary numbers 786, 480, 713 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.