Highest Common Factor of 742, 212, 278 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 742, 212, 278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 742, 212, 278 is 2 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 742, 212, 278 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 742, 212, 278 is 2.

HCF(742, 212, 278) = 2

HCF of 742, 212, 278 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 742, 212, 278 is 2.

Highest Common Factor of 742,212,278 using Euclid's algorithm

Highest Common Factor of 742,212,278 is 2

Step 1: Since 742 > 212, we apply the division lemma to 742 and 212, to get

742 = 212 x 3 + 106

Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 106 and 212, to get

212 = 106 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 106, the HCF of 742 and 212 is 106

Notice that 106 = HCF(212,106) = HCF(742,212) .

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

Step 1: Since 278 > 106, we apply the division lemma to 278 and 106, to get

278 = 106 x 2 + 66

Step 2: Since the reminder 106 ≠ 0, we apply division lemma to 66 and 106, to get

106 = 66 x 1 + 40

Step 3: We consider the new divisor 66 and the new remainder 40, and apply the division lemma to get

66 = 40 x 1 + 26

We consider the new divisor 40 and the new remainder 26,and apply the division lemma to get

40 = 26 x 1 + 14

We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 106 and 278 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(66,40) = HCF(106,66) = HCF(278,106) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 742, 212, 278 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 742, 212, 278?

Answer: HCF of 742, 212, 278 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 742, 212, 278 using Euclid's Algorithm?

Answer: For arbitrary numbers 742, 212, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.