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 418, 662, 826 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 418, 662, 826 is 2 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 418, 662, 826 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 418, 662, 826 is 2.
HCF(418, 662, 826) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 418, 662, 826 is 2.
Step 1: Since 662 > 418, we apply the division lemma to 662 and 418, to get
662 = 418 x 1 + 244
Step 2: Since the reminder 418 ≠ 0, we apply division lemma to 244 and 418, to get
418 = 244 x 1 + 174
Step 3: We consider the new divisor 244 and the new remainder 174, and apply the division lemma to get
244 = 174 x 1 + 70
We consider the new divisor 174 and the new remainder 70,and apply the division lemma to get
174 = 70 x 2 + 34
We consider the new divisor 70 and the new remainder 34,and apply the division lemma to get
70 = 34 x 2 + 2
We consider the new divisor 34 and the new remainder 2,and apply the division lemma to get
34 = 2 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 418 and 662 is 2
Notice that 2 = HCF(34,2) = HCF(70,34) = HCF(174,70) = HCF(244,174) = HCF(418,244) = HCF(662,418) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 826 > 2, we apply the division lemma to 826 and 2, to get
826 = 2 x 413 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 826 is 2
Notice that 2 = HCF(826,2) .
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 418, 662, 826?
Answer: HCF of 418, 662, 826 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 418, 662, 826 using Euclid's Algorithm?
Answer: For arbitrary numbers 418, 662, 826 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.