Highest Common Factor of 109, 176, 106 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 109, 176, 106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 109, 176, 106 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 109, 176, 106 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 109, 176, 106 is 1.
HCF(109, 176, 106) = 1
HCF of 109, 176, 106 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 109, 176, 106 is 1.
Highest Common Factor of 109,176,106 is 1
Step 1: Since 176 > 109, we apply the division lemma to 176 and 109, to get
176 = 109 x 1 + 67
Step 2: Since the reminder 109 ≠ 0, we apply division lemma to 67 and 109, to get
109 = 67 x 1 + 42
Step 3: We consider the new divisor 67 and the new remainder 42, and apply the division lemma to get
67 = 42 x 1 + 25
We consider the new divisor 42 and the new remainder 25,and apply the division lemma to get
42 = 25 x 1 + 17
We consider the new divisor 25 and the new remainder 17,and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 109 and 176 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(42,25) = HCF(67,42) = HCF(109,67) = HCF(176,109) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 1, we apply the division lemma to 106 and 1, to get
106 = 1 x 106 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 106 is 1
Notice that 1 = HCF(106,1) .
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Frequently Asked Questions on HCF of 109, 176, 106 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 109, 176, 106?
Answer: HCF of 109, 176, 106 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 109, 176, 106 using Euclid's Algorithm?
Answer: For arbitrary numbers 109, 176, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.