Highest Common Factor of 68, 316, 414 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 68, 316, 414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 68, 316, 414 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 68, 316, 414 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 68, 316, 414 is 2.
HCF(68, 316, 414) = 2
HCF of 68, 316, 414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 68, 316, 414 is 2.
Highest Common Factor of 68,316,414 is 2
Step 1: Since 316 > 68, we apply the division lemma to 316 and 68, to get
316 = 68 x 4 + 44
Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 44 and 68, to get
68 = 44 x 1 + 24
Step 3: We consider the new divisor 44 and the new remainder 24, and apply the division lemma to get
44 = 24 x 1 + 20
We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get
24 = 20 x 1 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 68 and 316 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(44,24) = HCF(68,44) = HCF(316,68) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 4, we apply the division lemma to 414 and 4, to get
414 = 4 x 103 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 414 is 2
Notice that 2 = HCF(4,2) = HCF(414,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 68, 316, 414 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 68, 316, 414?
Answer: HCF of 68, 316, 414 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 68, 316, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 68, 316, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
