Highest Common Factor of 374, 269 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 374, 269 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 374, 269 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 374, 269 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 374, 269 is 1.
HCF(374, 269) = 1
HCF of 374, 269 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 374, 269 is 1.
Highest Common Factor of 374,269 is 1
Step 1: Since 374 > 269, we apply the division lemma to 374 and 269, to get
374 = 269 x 1 + 105
Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 105 and 269, to get
269 = 105 x 2 + 59
Step 3: We consider the new divisor 105 and the new remainder 59, and apply the division lemma to get
105 = 59 x 1 + 46
We consider the new divisor 59 and the new remainder 46,and apply the division lemma to get
59 = 46 x 1 + 13
We consider the new divisor 46 and the new remainder 13,and apply the division lemma to get
46 = 13 x 3 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 374 and 269 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(46,13) = HCF(59,46) = HCF(105,59) = HCF(269,105) = HCF(374,269) .
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Frequently Asked Questions on HCF of 374, 269 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 374, 269?
Answer: HCF of 374, 269 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 374, 269 using Euclid's Algorithm?
Answer: For arbitrary numbers 374, 269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.