Highest Common Factor of 185, 666, 408, 14 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 185, 666, 408, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 185, 666, 408, 14 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 185, 666, 408, 14 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 185, 666, 408, 14 is 1.
HCF(185, 666, 408, 14) = 1
HCF of 185, 666, 408, 14 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 185, 666, 408, 14 is 1.
Highest Common Factor of 185,666,408,14 is 1
Step 1: Since 666 > 185, we apply the division lemma to 666 and 185, to get
666 = 185 x 3 + 111
Step 2: Since the reminder 185 ≠ 0, we apply division lemma to 111 and 185, to get
185 = 111 x 1 + 74
Step 3: We consider the new divisor 111 and the new remainder 74, and apply the division lemma to get
111 = 74 x 1 + 37
We consider the new divisor 74 and the new remainder 37, and apply the division lemma to get
74 = 37 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 37, the HCF of 185 and 666 is 37
Notice that 37 = HCF(74,37) = HCF(111,74) = HCF(185,111) = HCF(666,185) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 408 > 37, we apply the division lemma to 408 and 37, to get
408 = 37 x 11 + 1
Step 2: Since the reminder 37 ≠ 0, we apply division lemma to 1 and 37, to get
37 = 1 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 37 and 408 is 1
Notice that 1 = HCF(37,1) = HCF(408,37) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1
Notice that 1 = HCF(14,1) .
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Frequently Asked Questions on HCF of 185, 666, 408, 14 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 185, 666, 408, 14?
Answer: HCF of 185, 666, 408, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 185, 666, 408, 14 using Euclid's Algorithm?
Answer: For arbitrary numbers 185, 666, 408, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.