Highest Common Factor of 123, 966, 184 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 123, 966, 184 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 123, 966, 184 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 123, 966, 184 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 123, 966, 184 is 1.
HCF(123, 966, 184) = 1
HCF of 123, 966, 184 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 123, 966, 184 is 1.
Highest Common Factor of 123,966,184 is 1
Step 1: Since 966 > 123, we apply the division lemma to 966 and 123, to get
966 = 123 x 7 + 105
Step 2: Since the reminder 123 ≠ 0, we apply division lemma to 105 and 123, to get
123 = 105 x 1 + 18
Step 3: We consider the new divisor 105 and the new remainder 18, and apply the division lemma to get
105 = 18 x 5 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 123 and 966 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(105,18) = HCF(123,105) = HCF(966,123) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 184 > 3, we apply the division lemma to 184 and 3, to get
184 = 3 x 61 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 184 is 1
Notice that 1 = HCF(3,1) = HCF(184,3) .
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Frequently Asked Questions on HCF of 123, 966, 184 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 123, 966, 184?
Answer: HCF of 123, 966, 184 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 123, 966, 184 using Euclid's Algorithm?
Answer: For arbitrary numbers 123, 966, 184 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.