Highest Common Factor of 309, 255, 666 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 309, 255, 666 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 255, 666 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 309, 255, 666 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 309, 255, 666 is 3.
HCF(309, 255, 666) = 3
HCF of 309, 255, 666 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 255, 666 is 3.
Highest Common Factor of 309,255,666 is 3
Step 1: Since 309 > 255, we apply the division lemma to 309 and 255, to get
309 = 255 x 1 + 54
Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 54 and 255, to get
255 = 54 x 4 + 39
Step 3: We consider the new divisor 54 and the new remainder 39, and apply the division lemma to get
54 = 39 x 1 + 15
We consider the new divisor 39 and the new remainder 15,and apply the division lemma to get
39 = 15 x 2 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 309 and 255 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(54,39) = HCF(255,54) = HCF(309,255) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 666 > 3, we apply the division lemma to 666 and 3, to get
666 = 3 x 222 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 666 is 3
Notice that 3 = HCF(666,3) .
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Frequently Asked Questions on HCF of 309, 255, 666 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 309, 255, 666?
Answer: HCF of 309, 255, 666 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 255, 666 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 255, 666 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.