Highest Common Factor of 440, 842, 760 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 440, 842, 760 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 440, 842, 760 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 440, 842, 760 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 440, 842, 760 is 2.

HCF(440, 842, 760) = 2

HCF of 440, 842, 760 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 440, 842, 760 is 2.

Highest Common Factor of 440,842,760 using Euclid's algorithm

Highest Common Factor of 440,842,760 is 2

Step 1: Since 842 > 440, we apply the division lemma to 842 and 440, to get

842 = 440 x 1 + 402

Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 402 and 440, to get

440 = 402 x 1 + 38

Step 3: We consider the new divisor 402 and the new remainder 38, and apply the division lemma to get

402 = 38 x 10 + 22

We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get

38 = 22 x 1 + 16

We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get

22 = 16 x 1 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 440 and 842 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(402,38) = HCF(440,402) = HCF(842,440) .

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

Step 1: Since 760 > 2, we apply the division lemma to 760 and 2, to get

760 = 2 x 380 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 760 is 2

Notice that 2 = HCF(760,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 440, 842, 760 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 440, 842, 760?

Answer: HCF of 440, 842, 760 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 440, 842, 760 using Euclid's Algorithm?

Answer: For arbitrary numbers 440, 842, 760 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.