Highest Common Factor of 706, 414, 878 using Euclid's algorithm
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 706, 414, 878 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 706, 414, 878 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 706, 414, 878 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 706, 414, 878 is 2.
HCF(706, 414, 878) = 2
HCF of 706, 414, 878 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 706, 414, 878 is 2.
Highest Common Factor of 706,414,878 is 2
Step 1: Since 706 > 414, we apply the division lemma to 706 and 414, to get
706 = 414 x 1 + 292
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 292 and 414, to get
414 = 292 x 1 + 122
Step 3: We consider the new divisor 292 and the new remainder 122, and apply the division lemma to get
292 = 122 x 2 + 48
We consider the new divisor 122 and the new remainder 48,and apply the division lemma to get
122 = 48 x 2 + 26
We consider the new divisor 48 and the new remainder 26,and apply the division lemma to get
48 = 26 x 1 + 22
We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get
26 = 22 x 1 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 706 and 414 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(48,26) = HCF(122,48) = HCF(292,122) = HCF(414,292) = HCF(706,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 878 > 2, we apply the division lemma to 878 and 2, to get
878 = 2 x 439 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 878 is 2
Notice that 2 = HCF(878,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 706, 414, 878 using Euclid's Algorithm
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 706, 414, 878?
Answer: HCF of 706, 414, 878 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 706, 414, 878 using Euclid's Algorithm?
Answer: For arbitrary numbers 706, 414, 878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.