Highest Common Factor of 382, 280 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 382, 280 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 382, 280 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 382, 280 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 382, 280 is 2.
HCF(382, 280) = 2
HCF of 382, 280 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 382, 280 is 2.
Highest Common Factor of 382,280 is 2
Step 1: Since 382 > 280, we apply the division lemma to 382 and 280, to get
382 = 280 x 1 + 102
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 102 and 280, to get
280 = 102 x 2 + 76
Step 3: We consider the new divisor 102 and the new remainder 76, and apply the division lemma to get
102 = 76 x 1 + 26
We consider the new divisor 76 and the new remainder 26,and apply the division lemma to get
76 = 26 x 2 + 24
We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 382 and 280 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(76,26) = HCF(102,76) = HCF(280,102) = HCF(382,280) .
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Frequently Asked Questions on HCF of 382, 280 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 382, 280?
Answer: HCF of 382, 280 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 382, 280 using Euclid's Algorithm?
Answer: For arbitrary numbers 382, 280 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.