Highest Common Factor of 270, 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 270, 382 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 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 270, 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 270, 382 is 2.
HCF(270, 382) = 2
HCF of 270, 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 270, 382 is 2.
Highest Common Factor of 270,382 is 2
Step 1: Since 382 > 270, we apply the division lemma to 382 and 270, to get
382 = 270 x 1 + 112
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 112 and 270, to get
270 = 112 x 2 + 46
Step 3: We consider the new divisor 112 and the new remainder 46, and apply the division lemma to get
112 = 46 x 2 + 20
We consider the new divisor 46 and the new remainder 20,and apply the division lemma to get
46 = 20 x 2 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 270 and 382 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(46,20) = HCF(112,46) = HCF(270,112) = HCF(382,270) .
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Frequently Asked Questions on HCF of 270, 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 270, 382?
Answer: HCF of 270, 382 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 382 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 382 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.