Highest Common Factor of 368, 464, 185 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 368, 464, 185 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 368, 464, 185 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 368, 464, 185 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 368, 464, 185 is 1.
HCF(368, 464, 185) = 1
HCF of 368, 464, 185 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 368, 464, 185 is 1.
Highest Common Factor of 368,464,185 is 1
Step 1: Since 464 > 368, we apply the division lemma to 464 and 368, to get
464 = 368 x 1 + 96
Step 2: Since the reminder 368 ≠ 0, we apply division lemma to 96 and 368, to get
368 = 96 x 3 + 80
Step 3: We consider the new divisor 96 and the new remainder 80, and apply the division lemma to get
96 = 80 x 1 + 16
We consider the new divisor 80 and the new remainder 16, and apply the division lemma to get
80 = 16 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 368 and 464 is 16
Notice that 16 = HCF(80,16) = HCF(96,80) = HCF(368,96) = HCF(464,368) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 185 > 16, we apply the division lemma to 185 and 16, to get
185 = 16 x 11 + 9
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 9 and 16, to get
16 = 9 x 1 + 7
Step 3: We consider the new divisor 9 and the new remainder 7, and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 185 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(185,16) .
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Frequently Asked Questions on HCF of 368, 464, 185 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 368, 464, 185?
Answer: HCF of 368, 464, 185 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 368, 464, 185 using Euclid's Algorithm?
Answer: For arbitrary numbers 368, 464, 185 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
