Highest Common Factor of 288, 414, 853 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 288, 414, 853 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 288, 414, 853 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 288, 414, 853 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 288, 414, 853 is 1.

HCF(288, 414, 853) = 1

HCF of 288, 414, 853 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 288, 414, 853 is 1.

Highest Common Factor of 288,414,853 using Euclid's algorithm

Highest Common Factor of 288,414,853 is 1

Step 1: Since 414 > 288, we apply the division lemma to 414 and 288, to get

414 = 288 x 1 + 126

Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 126 and 288, to get

288 = 126 x 2 + 36

Step 3: We consider the new divisor 126 and the new remainder 36, and apply the division lemma to get

126 = 36 x 3 + 18

We consider the new divisor 36 and the new remainder 18, and apply the division lemma to get

36 = 18 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 288 and 414 is 18

Notice that 18 = HCF(36,18) = HCF(126,36) = HCF(288,126) = HCF(414,288) .

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

Step 1: Since 853 > 18, we apply the division lemma to 853 and 18, to get

853 = 18 x 47 + 7

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 7 and 18, to get

18 = 7 x 2 + 4

Step 3: We consider the new divisor 7 and the new remainder 4, and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 18 and 853 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(853,18) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 288, 414, 853 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 288, 414, 853?

Answer: HCF of 288, 414, 853 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 288, 414, 853 using Euclid's Algorithm?

Answer: For arbitrary numbers 288, 414, 853 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.