Highest Common Factor of 440, 695, 332 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, 695, 332 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 440, 695, 332 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 440, 695, 332 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, 695, 332 is 1.

HCF(440, 695, 332) = 1

HCF of 440, 695, 332 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, 695, 332 is 1.

Highest Common Factor of 440,695,332 using Euclid's algorithm

Highest Common Factor of 440,695,332 is 1

Step 1: Since 695 > 440, we apply the division lemma to 695 and 440, to get

695 = 440 x 1 + 255

Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 255 and 440, to get

440 = 255 x 1 + 185

Step 3: We consider the new divisor 255 and the new remainder 185, and apply the division lemma to get

255 = 185 x 1 + 70

We consider the new divisor 185 and the new remainder 70,and apply the division lemma to get

185 = 70 x 2 + 45

We consider the new divisor 70 and the new remainder 45,and apply the division lemma to get

70 = 45 x 1 + 25

We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get

45 = 25 x 1 + 20

We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get

25 = 20 x 1 + 5

We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 440 and 695 is 5

Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(70,45) = HCF(185,70) = HCF(255,185) = HCF(440,255) = HCF(695,440) .

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

Step 1: Since 332 > 5, we apply the division lemma to 332 and 5, to get

332 = 5 x 66 + 2

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

5 = 2 x 2 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 332 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(332,5) .

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, 695, 332 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, 695, 332?

Answer: HCF of 440, 695, 332 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 440, 695, 332 using Euclid's Algorithm?

Answer: For arbitrary numbers 440, 695, 332 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.