Highest Common Factor of 338, 2640, 8381 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 338, 2640, 8381 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 2640, 8381 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 338, 2640, 8381 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 338, 2640, 8381 is 1.
HCF(338, 2640, 8381) = 1
HCF of 338, 2640, 8381 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 338, 2640, 8381 is 1.
Highest Common Factor of 338,2640,8381 is 1
Step 1: Since 2640 > 338, we apply the division lemma to 2640 and 338, to get
2640 = 338 x 7 + 274
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 274 and 338, to get
338 = 274 x 1 + 64
Step 3: We consider the new divisor 274 and the new remainder 64, and apply the division lemma to get
274 = 64 x 4 + 18
We consider the new divisor 64 and the new remainder 18,and apply the division lemma to get
64 = 18 x 3 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 338 and 2640 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(64,18) = HCF(274,64) = HCF(338,274) = HCF(2640,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8381 > 2, we apply the division lemma to 8381 and 2, to get
8381 = 2 x 4190 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 8381 is 1
Notice that 1 = HCF(2,1) = HCF(8381,2) .
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Frequently Asked Questions on HCF of 338, 2640, 8381 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 338, 2640, 8381?
Answer: HCF of 338, 2640, 8381 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 2640, 8381 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 2640, 8381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.