Highest Common Factor of 360, 418, 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 360, 418, 185 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 418, 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 360, 418, 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 360, 418, 185 is 1.
HCF(360, 418, 185) = 1
HCF of 360, 418, 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 360, 418, 185 is 1.
Highest Common Factor of 360,418,185 is 1
Step 1: Since 418 > 360, we apply the division lemma to 418 and 360, to get
418 = 360 x 1 + 58
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 58 and 360, to get
360 = 58 x 6 + 12
Step 3: We consider the new divisor 58 and the new remainder 12, and apply the division lemma to get
58 = 12 x 4 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 360 and 418 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(58,12) = HCF(360,58) = HCF(418,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 185 > 2, we apply the division lemma to 185 and 2, to get
185 = 2 x 92 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 185 is 1
Notice that 1 = HCF(2,1) = HCF(185,2) .
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Frequently Asked Questions on HCF of 360, 418, 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 360, 418, 185?
Answer: HCF of 360, 418, 185 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 418, 185 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 418, 185 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.