Highest Common Factor of 186, 309, 555 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, 309, 555 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 186, 309, 555 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, 309, 555 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, 309, 555 is 3.
HCF(186, 309, 555) = 3
HCF of 186, 309, 555 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, 309, 555 is 3.
Highest Common Factor of 186,309,555 is 3
Step 1: Since 309 > 186, we apply the division lemma to 309 and 186, to get
309 = 186 x 1 + 123
Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 123 and 186, to get
186 = 123 x 1 + 63
Step 3: We consider the new divisor 123 and the new remainder 63, and apply the division lemma to get
123 = 63 x 1 + 60
We consider the new divisor 63 and the new remainder 60,and apply the division lemma to get
63 = 60 x 1 + 3
We consider the new divisor 60 and the new remainder 3,and apply the division lemma to get
60 = 3 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 186 and 309 is 3
Notice that 3 = HCF(60,3) = HCF(63,60) = HCF(123,63) = HCF(186,123) = HCF(309,186) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 555 > 3, we apply the division lemma to 555 and 3, to get
555 = 3 x 185 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 555 is 3
Notice that 3 = HCF(555,3) .
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Frequently Asked Questions on HCF of 186, 309, 555 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, 309, 555?
Answer: HCF of 186, 309, 555 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 186, 309, 555 using Euclid's Algorithm?
Answer: For arbitrary numbers 186, 309, 555 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.