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 718, 458, 409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 718, 458, 409 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 718, 458, 409 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 718, 458, 409 is 1.
HCF(718, 458, 409) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 718, 458, 409 is 1.
Step 1: Since 718 > 458, we apply the division lemma to 718 and 458, to get
718 = 458 x 1 + 260
Step 2: Since the reminder 458 ≠ 0, we apply division lemma to 260 and 458, to get
458 = 260 x 1 + 198
Step 3: We consider the new divisor 260 and the new remainder 198, and apply the division lemma to get
260 = 198 x 1 + 62
We consider the new divisor 198 and the new remainder 62,and apply the division lemma to get
198 = 62 x 3 + 12
We consider the new divisor 62 and the new remainder 12,and apply the division lemma to get
62 = 12 x 5 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 718 and 458 is 2
Notice that 2 = HCF(12,2) = HCF(62,12) = HCF(198,62) = HCF(260,198) = HCF(458,260) = HCF(718,458) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 409 > 2, we apply the division lemma to 409 and 2, to get
409 = 2 x 204 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 409 is 1
Notice that 1 = HCF(2,1) = HCF(409,2) .
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 718, 458, 409?
Answer: HCF of 718, 458, 409 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 718, 458, 409 using Euclid's Algorithm?
Answer: For arbitrary numbers 718, 458, 409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.