Highest Common Factor of 326, 5740 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 326, 5740 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 326, 5740 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 326, 5740 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 326, 5740 is 2.
HCF(326, 5740) = 2
HCF of 326, 5740 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 326, 5740 is 2.
Highest Common Factor of 326,5740 is 2
Step 1: Since 5740 > 326, we apply the division lemma to 5740 and 326, to get
5740 = 326 x 17 + 198
Step 2: Since the reminder 326 ≠ 0, we apply division lemma to 198 and 326, to get
326 = 198 x 1 + 128
Step 3: We consider the new divisor 198 and the new remainder 128, and apply the division lemma to get
198 = 128 x 1 + 70
We consider the new divisor 128 and the new remainder 70,and apply the division lemma to get
128 = 70 x 1 + 58
We consider the new divisor 70 and the new remainder 58,and apply the division lemma to get
70 = 58 x 1 + 12
We consider the new divisor 58 and the new remainder 12,and apply the division lemma to get
58 = 12 x 4 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 326 and 5740 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(58,12) = HCF(70,58) = HCF(128,70) = HCF(198,128) = HCF(326,198) = HCF(5740,326) .
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Frequently Asked Questions on HCF of 326, 5740 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 326, 5740?
Answer: HCF of 326, 5740 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 326, 5740 using Euclid's Algorithm?
Answer: For arbitrary numbers 326, 5740 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.