Highest Common Factor of 186, 372, 705 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 186, 372, 705 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 186, 372, 705 is 3 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 186, 372, 705 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 186, 372, 705 is 3.
HCF(186, 372, 705) = 3
HCF of 186, 372, 705 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 186, 372, 705 is 3.
Highest Common Factor of 186,372,705 is 3
Step 1: Since 372 > 186, we apply the division lemma to 372 and 186, to get
372 = 186 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 186, the HCF of 186 and 372 is 186
Notice that 186 = HCF(372,186) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 705 > 186, we apply the division lemma to 705 and 186, to get
705 = 186 x 3 + 147
Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 147 and 186, to get
186 = 147 x 1 + 39
Step 3: We consider the new divisor 147 and the new remainder 39, and apply the division lemma to get
147 = 39 x 3 + 30
We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get
39 = 30 x 1 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 186 and 705 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(147,39) = HCF(186,147) = HCF(705,186) .
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Frequently Asked Questions on HCF of 186, 372, 705 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 186, 372, 705?
Answer: HCF of 186, 372, 705 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 186, 372, 705 using Euclid's Algorithm?
Answer: For arbitrary numbers 186, 372, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
