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 406, 702, 114 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 406, 702, 114 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 406, 702, 114 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 406, 702, 114 is 2.
HCF(406, 702, 114) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 406, 702, 114 is 2.
Step 1: Since 702 > 406, we apply the division lemma to 702 and 406, to get
702 = 406 x 1 + 296
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 296 and 406, to get
406 = 296 x 1 + 110
Step 3: We consider the new divisor 296 and the new remainder 110, and apply the division lemma to get
296 = 110 x 2 + 76
We consider the new divisor 110 and the new remainder 76,and apply the division lemma to get
110 = 76 x 1 + 34
We consider the new divisor 76 and the new remainder 34,and apply the division lemma to get
76 = 34 x 2 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 406 and 702 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(76,34) = HCF(110,76) = HCF(296,110) = HCF(406,296) = HCF(702,406) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 114 > 2, we apply the division lemma to 114 and 2, to get
114 = 2 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 114 is 2
Notice that 2 = HCF(114,2) .
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 406, 702, 114?
Answer: HCF of 406, 702, 114 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 406, 702, 114 using Euclid's Algorithm?
Answer: For arbitrary numbers 406, 702, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.