Highest Common Factor of 787, 996, 742 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 787, 996, 742 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 787, 996, 742 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 787, 996, 742 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 787, 996, 742 is 1.

HCF(787, 996, 742) = 1

HCF of 787, 996, 742 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 787, 996, 742 is 1.

Highest Common Factor of 787,996,742 using Euclid's algorithm

Highest Common Factor of 787,996,742 is 1

Step 1: Since 996 > 787, we apply the division lemma to 996 and 787, to get

996 = 787 x 1 + 209

Step 2: Since the reminder 787 ≠ 0, we apply division lemma to 209 and 787, to get

787 = 209 x 3 + 160

Step 3: We consider the new divisor 209 and the new remainder 160, and apply the division lemma to get

209 = 160 x 1 + 49

We consider the new divisor 160 and the new remainder 49,and apply the division lemma to get

160 = 49 x 3 + 13

We consider the new divisor 49 and the new remainder 13,and apply the division lemma to get

49 = 13 x 3 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 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 787 and 996 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(49,13) = HCF(160,49) = HCF(209,160) = HCF(787,209) = HCF(996,787) .

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

Step 1: Since 742 > 1, we apply the division lemma to 742 and 1, to get

742 = 1 x 742 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 742 is 1

Notice that 1 = HCF(742,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 787, 996, 742 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 787, 996, 742?

Answer: HCF of 787, 996, 742 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 787, 996, 742 using Euclid's Algorithm?

Answer: For arbitrary numbers 787, 996, 742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.