Highest Common Factor of 912, 269, 865 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 912, 269, 865 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 912, 269, 865 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 912, 269, 865 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 912, 269, 865 is 1.
HCF(912, 269, 865) = 1
HCF of 912, 269, 865 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 912, 269, 865 is 1.
Highest Common Factor of 912,269,865 is 1
Step 1: Since 912 > 269, we apply the division lemma to 912 and 269, to get
912 = 269 x 3 + 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 912 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(912,269) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 865 > 1, we apply the division lemma to 865 and 1, to get
865 = 1 x 865 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 865 is 1
Notice that 1 = HCF(865,1) .
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Frequently Asked Questions on HCF of 912, 269, 865 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 912, 269, 865?
Answer: HCF of 912, 269, 865 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 912, 269, 865 using Euclid's Algorithm?
Answer: For arbitrary numbers 912, 269, 865 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.