Highest Common Factor of 8234, 382 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 8234, 382 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8234, 382 is 2 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 8234, 382 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 8234, 382 is 2.
HCF(8234, 382) = 2
HCF of 8234, 382 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8234, 382 is 2.
Highest Common Factor of 8234,382 is 2
Step 1: Since 8234 > 382, we apply the division lemma to 8234 and 382, to get
8234 = 382 x 21 + 212
Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 212 and 382, to get
382 = 212 x 1 + 170
Step 3: We consider the new divisor 212 and the new remainder 170, and apply the division lemma to get
212 = 170 x 1 + 42
We consider the new divisor 170 and the new remainder 42,and apply the division lemma to get
170 = 42 x 4 + 2
We consider the new divisor 42 and the new remainder 2,and apply the division lemma to get
42 = 2 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8234 and 382 is 2
Notice that 2 = HCF(42,2) = HCF(170,42) = HCF(212,170) = HCF(382,212) = HCF(8234,382) .
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Frequently Asked Questions on HCF of 8234, 382 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 8234, 382?
Answer: HCF of 8234, 382 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8234, 382 using Euclid's Algorithm?
Answer: For arbitrary numbers 8234, 382 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.