Highest Common Factor of 106, 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 106, 112 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 106, 112 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 106, 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 106, 112 is 2.
HCF(106, 112) = 2
HCF of 106, 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 106, 112 is 2.
Highest Common Factor of 106,112 is 2
Step 1: Since 112 > 106, we apply the division lemma to 112 and 106, to get
112 = 106 x 1 + 6
Step 2: Since the reminder 106 ≠ 0, we apply division lemma to 6 and 106, to get
106 = 6 x 17 + 4
Step 3: We consider the new divisor 6 and the new remainder 4, and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 106 and 112 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(106,6) = HCF(112,106) .
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Frequently Asked Questions on HCF of 106, 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 106, 112?
Answer: HCF of 106, 112 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 106, 112 using Euclid's Algorithm?
Answer: For arbitrary numbers 106, 112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.