Highest Common Factor of 184, 668 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 184, 668 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 184, 668 is 4 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 184, 668 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 184, 668 is 4.
HCF(184, 668) = 4
HCF of 184, 668 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 184, 668 is 4.
Highest Common Factor of 184,668 is 4
Step 1: Since 668 > 184, we apply the division lemma to 668 and 184, to get
668 = 184 x 3 + 116
Step 2: Since the reminder 184 ≠ 0, we apply division lemma to 116 and 184, to get
184 = 116 x 1 + 68
Step 3: We consider the new divisor 116 and the new remainder 68, and apply the division lemma to get
116 = 68 x 1 + 48
We consider the new divisor 68 and the new remainder 48,and apply the division lemma to get
68 = 48 x 1 + 20
We consider the new divisor 48 and the new remainder 20,and apply the division lemma to get
48 = 20 x 2 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 184 and 668 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(48,20) = HCF(68,48) = HCF(116,68) = HCF(184,116) = HCF(668,184) .
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Frequently Asked Questions on HCF of 184, 668 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 184, 668?
Answer: HCF of 184, 668 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 184, 668 using Euclid's Algorithm?
Answer: For arbitrary numbers 184, 668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.