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 865, 330, 282 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 865, 330, 282 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 865, 330, 282 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 865, 330, 282 is 1.
HCF(865, 330, 282) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 865, 330, 282 is 1.
Step 1: Since 865 > 330, we apply the division lemma to 865 and 330, to get
865 = 330 x 2 + 205
Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 205 and 330, to get
330 = 205 x 1 + 125
Step 3: We consider the new divisor 205 and the new remainder 125, and apply the division lemma to get
205 = 125 x 1 + 80
We consider the new divisor 125 and the new remainder 80,and apply the division lemma to get
125 = 80 x 1 + 45
We consider the new divisor 80 and the new remainder 45,and apply the division lemma to get
80 = 45 x 1 + 35
We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get
45 = 35 x 1 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 865 and 330 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(80,45) = HCF(125,80) = HCF(205,125) = HCF(330,205) = HCF(865,330) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 282 > 5, we apply the division lemma to 282 and 5, to get
282 = 5 x 56 + 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 282 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(282,5) .
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 865, 330, 282?
Answer: HCF of 865, 330, 282 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 865, 330, 282 using Euclid's Algorithm?
Answer: For arbitrary numbers 865, 330, 282 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.