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 339, 914, 212 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 339, 914, 212 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 339, 914, 212 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 339, 914, 212 is 1.
HCF(339, 914, 212) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 339, 914, 212 is 1.
Step 1: Since 914 > 339, we apply the division lemma to 914 and 339, to get
914 = 339 x 2 + 236
Step 2: Since the reminder 339 ≠ 0, we apply division lemma to 236 and 339, to get
339 = 236 x 1 + 103
Step 3: We consider the new divisor 236 and the new remainder 103, and apply the division lemma to get
236 = 103 x 2 + 30
We consider the new divisor 103 and the new remainder 30,and apply the division lemma to get
103 = 30 x 3 + 13
We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get
30 = 13 x 2 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 339 and 914 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(103,30) = HCF(236,103) = HCF(339,236) = HCF(914,339) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 212 > 1, we apply the division lemma to 212 and 1, to get
212 = 1 x 212 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 212 is 1
Notice that 1 = HCF(212,1) .
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 339, 914, 212?
Answer: HCF of 339, 914, 212 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 339, 914, 212 using Euclid's Algorithm?
Answer: For arbitrary numbers 339, 914, 212 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.