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 839, 214, 360 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 839, 214, 360 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 839, 214, 360 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 839, 214, 360 is 1.
HCF(839, 214, 360) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 839, 214, 360 is 1.
Step 1: Since 839 > 214, we apply the division lemma to 839 and 214, to get
839 = 214 x 3 + 197
Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 197 and 214, to get
214 = 197 x 1 + 17
Step 3: We consider the new divisor 197 and the new remainder 17, and apply the division lemma to get
197 = 17 x 11 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 839 and 214 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(197,17) = HCF(214,197) = HCF(839,214) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 360 > 1, we apply the division lemma to 360 and 1, to get
360 = 1 x 360 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 360 is 1
Notice that 1 = HCF(360,1) .
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 839, 214, 360?
Answer: HCF of 839, 214, 360 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 839, 214, 360 using Euclid's Algorithm?
Answer: For arbitrary numbers 839, 214, 360 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.