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 286, 165, 294 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 286, 165, 294 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 286, 165, 294 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 286, 165, 294 is 1.
HCF(286, 165, 294) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 286, 165, 294 is 1.
Step 1: Since 286 > 165, we apply the division lemma to 286 and 165, to get
286 = 165 x 1 + 121
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 121 and 165, to get
165 = 121 x 1 + 44
Step 3: We consider the new divisor 121 and the new remainder 44, and apply the division lemma to get
121 = 44 x 2 + 33
We consider the new divisor 44 and the new remainder 33,and apply the division lemma to get
44 = 33 x 1 + 11
We consider the new divisor 33 and the new remainder 11,and apply the division lemma to get
33 = 11 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 286 and 165 is 11
Notice that 11 = HCF(33,11) = HCF(44,33) = HCF(121,44) = HCF(165,121) = HCF(286,165) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 294 > 11, we apply the division lemma to 294 and 11, to get
294 = 11 x 26 + 8
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 8 and 11, to get
11 = 8 x 1 + 3
Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 11 and 294 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(294,11) .
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 286, 165, 294?
Answer: HCF of 286, 165, 294 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 286, 165, 294 using Euclid's Algorithm?
Answer: For arbitrary numbers 286, 165, 294 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.