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 555, 410, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 555, 410, 309 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 555, 410, 309 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 555, 410, 309 is 1.
HCF(555, 410, 309) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 555, 410, 309 is 1.
Step 1: Since 555 > 410, we apply the division lemma to 555 and 410, to get
555 = 410 x 1 + 145
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 145 and 410, to get
410 = 145 x 2 + 120
Step 3: We consider the new divisor 145 and the new remainder 120, and apply the division lemma to get
145 = 120 x 1 + 25
We consider the new divisor 120 and the new remainder 25,and apply the division lemma to get
120 = 25 x 4 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 555 and 410 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(120,25) = HCF(145,120) = HCF(410,145) = HCF(555,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 309 > 5, we apply the division lemma to 309 and 5, to get
309 = 5 x 61 + 4
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get
5 = 4 x 1 + 1
Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 309 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(309,5) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 555, 410, 309?
Answer: HCF of 555, 410, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 555, 410, 309 using Euclid's Algorithm?
Answer: For arbitrary numbers 555, 410, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.