Highest Common Factor of 912, 343, 112 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, 343, 112 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 912, 343, 112 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, 343, 112 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, 343, 112 is 1.
HCF(912, 343, 112) = 1
HCF of 912, 343, 112 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, 343, 112 is 1.
Highest Common Factor of 912,343,112 is 1
Step 1: Since 912 > 343, we apply the division lemma to 912 and 343, to get
912 = 343 x 2 + 226
Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 226 and 343, to get
343 = 226 x 1 + 117
Step 3: We consider the new divisor 226 and the new remainder 117, and apply the division lemma to get
226 = 117 x 1 + 109
We consider the new divisor 117 and the new remainder 109,and apply the division lemma to get
117 = 109 x 1 + 8
We consider the new divisor 109 and the new remainder 8,and apply the division lemma to get
109 = 8 x 13 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 912 and 343 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(109,8) = HCF(117,109) = HCF(226,117) = HCF(343,226) = HCF(912,343) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 112 > 1, we apply the division lemma to 112 and 1, to get
112 = 1 x 112 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 112 is 1
Notice that 1 = HCF(112,1) .
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Frequently Asked Questions on HCF of 912, 343, 112 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, 343, 112?
Answer: HCF of 912, 343, 112 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 912, 343, 112 using Euclid's Algorithm?
Answer: For arbitrary numbers 912, 343, 112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.