Highest Common Factor of 212, 1045, 1834 using Euclid's algorithm
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 212, 1045, 1834 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 212, 1045, 1834 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 212, 1045, 1834 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 212, 1045, 1834 is 1.
HCF(212, 1045, 1834) = 1
HCF of 212, 1045, 1834 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 212, 1045, 1834 is 1.
Highest Common Factor of 212,1045,1834 is 1
Step 1: Since 1045 > 212, we apply the division lemma to 1045 and 212, to get
1045 = 212 x 4 + 197
Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 197 and 212, to get
212 = 197 x 1 + 15
Step 3: We consider the new divisor 197 and the new remainder 15, and apply the division lemma to get
197 = 15 x 13 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 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 212 and 1045 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(197,15) = HCF(212,197) = HCF(1045,212) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1834 > 1, we apply the division lemma to 1834 and 1, to get
1834 = 1 x 1834 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1834 is 1
Notice that 1 = HCF(1834,1) .
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Frequently Asked Questions on HCF of 212, 1045, 1834 using Euclid's Algorithm
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 212, 1045, 1834?
Answer: HCF of 212, 1045, 1834 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 212, 1045, 1834 using Euclid's Algorithm?
Answer: For arbitrary numbers 212, 1045, 1834 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.