Highest Common Factor of 268, 37409 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 268, 37409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 268, 37409 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 268, 37409 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 268, 37409 is 1.
HCF(268, 37409) = 1
HCF of 268, 37409 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 268, 37409 is 1.
Highest Common Factor of 268,37409 is 1
Step 1: Since 37409 > 268, we apply the division lemma to 37409 and 268, to get
37409 = 268 x 139 + 157
Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 157 and 268, to get
268 = 157 x 1 + 111
Step 3: We consider the new divisor 157 and the new remainder 111, and apply the division lemma to get
157 = 111 x 1 + 46
We consider the new divisor 111 and the new remainder 46,and apply the division lemma to get
111 = 46 x 2 + 19
We consider the new divisor 46 and the new remainder 19,and apply the division lemma to get
46 = 19 x 2 + 8
We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get
19 = 8 x 2 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 268 and 37409 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(46,19) = HCF(111,46) = HCF(157,111) = HCF(268,157) = HCF(37409,268) .
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Frequently Asked Questions on HCF of 268, 37409 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 268, 37409?
Answer: HCF of 268, 37409 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 268, 37409 using Euclid's Algorithm?
Answer: For arbitrary numbers 268, 37409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.