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 414, 71468 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 71468 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 414, 71468 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 414, 71468 is 2.
HCF(414, 71468) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 71468 is 2.
Step 1: Since 71468 > 414, we apply the division lemma to 71468 and 414, to get
71468 = 414 x 172 + 260
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 260 and 414, to get
414 = 260 x 1 + 154
Step 3: We consider the new divisor 260 and the new remainder 154, and apply the division lemma to get
260 = 154 x 1 + 106
We consider the new divisor 154 and the new remainder 106,and apply the division lemma to get
154 = 106 x 1 + 48
We consider the new divisor 106 and the new remainder 48,and apply the division lemma to get
106 = 48 x 2 + 10
We consider the new divisor 48 and the new remainder 10,and apply the division lemma to get
48 = 10 x 4 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 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 414 and 71468 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(48,10) = HCF(106,48) = HCF(154,106) = HCF(260,154) = HCF(414,260) = HCF(71468,414) .
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 414, 71468?
Answer: HCF of 414, 71468 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 71468 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 71468 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.