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 905, 589, 784 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 589, 784 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 905, 589, 784 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 905, 589, 784 is 1.
HCF(905, 589, 784) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 905, 589, 784 is 1.
Step 1: Since 905 > 589, we apply the division lemma to 905 and 589, to get
905 = 589 x 1 + 316
Step 2: Since the reminder 589 ≠ 0, we apply division lemma to 316 and 589, to get
589 = 316 x 1 + 273
Step 3: We consider the new divisor 316 and the new remainder 273, and apply the division lemma to get
316 = 273 x 1 + 43
We consider the new divisor 273 and the new remainder 43,and apply the division lemma to get
273 = 43 x 6 + 15
We consider the new divisor 43 and the new remainder 15,and apply the division lemma to get
43 = 15 x 2 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 1
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 905 and 589 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(273,43) = HCF(316,273) = HCF(589,316) = HCF(905,589) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 784 > 1, we apply the division lemma to 784 and 1, to get
784 = 1 x 784 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 784 is 1
Notice that 1 = HCF(784,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 905, 589, 784?
Answer: HCF of 905, 589, 784 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 589, 784 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 589, 784 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.