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 411, 713, 101 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 411, 713, 101 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 411, 713, 101 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 411, 713, 101 is 1.
HCF(411, 713, 101) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 411, 713, 101 is 1.
Step 1: Since 713 > 411, we apply the division lemma to 713 and 411, to get
713 = 411 x 1 + 302
Step 2: Since the reminder 411 ≠ 0, we apply division lemma to 302 and 411, to get
411 = 302 x 1 + 109
Step 3: We consider the new divisor 302 and the new remainder 109, and apply the division lemma to get
302 = 109 x 2 + 84
We consider the new divisor 109 and the new remainder 84,and apply the division lemma to get
109 = 84 x 1 + 25
We consider the new divisor 84 and the new remainder 25,and apply the division lemma to get
84 = 25 x 3 + 9
We consider the new divisor 25 and the new remainder 9,and apply the division lemma to get
25 = 9 x 2 + 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 411 and 713 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(25,9) = HCF(84,25) = HCF(109,84) = HCF(302,109) = HCF(411,302) = HCF(713,411) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 101 > 1, we apply the division lemma to 101 and 1, to get
101 = 1 x 101 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 101 is 1
Notice that 1 = HCF(101,1) .
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 411, 713, 101?
Answer: HCF of 411, 713, 101 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 411, 713, 101 using Euclid's Algorithm?
Answer: For arbitrary numbers 411, 713, 101 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.