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, 821, 69 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 821, 69 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 309, 821, 69 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, 821, 69 is 1.
HCF(309, 821, 69) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 821, 69 is 1.
Step 1: Since 821 > 309, we apply the division lemma to 821 and 309, to get
821 = 309 x 2 + 203
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 203 and 309, to get
309 = 203 x 1 + 106
Step 3: We consider the new divisor 203 and the new remainder 106, and apply the division lemma to get
203 = 106 x 1 + 97
We consider the new divisor 106 and the new remainder 97,and apply the division lemma to get
106 = 97 x 1 + 9
We consider the new divisor 97 and the new remainder 9,and apply the division lemma to get
97 = 9 x 10 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 309 and 821 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(97,9) = HCF(106,97) = HCF(203,106) = HCF(309,203) = HCF(821,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69 > 1, we apply the division lemma to 69 and 1, to get
69 = 1 x 69 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 69 is 1
Notice that 1 = HCF(69,1) .
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 309, 821, 69?
Answer: HCF of 309, 821, 69 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 821, 69 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 821, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.