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 459, 652, 113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 652, 113 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 459, 652, 113 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 459, 652, 113 is 1.
HCF(459, 652, 113) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 459, 652, 113 is 1.
Step 1: Since 652 > 459, we apply the division lemma to 652 and 459, to get
652 = 459 x 1 + 193
Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 193 and 459, to get
459 = 193 x 2 + 73
Step 3: We consider the new divisor 193 and the new remainder 73, and apply the division lemma to get
193 = 73 x 2 + 47
We consider the new divisor 73 and the new remainder 47,and apply the division lemma to get
73 = 47 x 1 + 26
We consider the new divisor 47 and the new remainder 26,and apply the division lemma to get
47 = 26 x 1 + 21
We consider the new divisor 26 and the new remainder 21,and apply the division lemma to get
26 = 21 x 1 + 5
We consider the new divisor 21 and the new remainder 5,and apply the division lemma to get
21 = 5 x 4 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 459 and 652 is 1
Notice that 1 = HCF(5,1) = HCF(21,5) = HCF(26,21) = HCF(47,26) = HCF(73,47) = HCF(193,73) = HCF(459,193) = HCF(652,459) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 113 > 1, we apply the division lemma to 113 and 1, to get
113 = 1 x 113 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 113 is 1
Notice that 1 = HCF(113,1) .
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 459, 652, 113?
Answer: HCF of 459, 652, 113 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 652, 113 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 652, 113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.