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 5407, 3074, 96368 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5407, 3074, 96368 is 1 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 5407, 3074, 96368 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 5407, 3074, 96368 is 1.
HCF(5407, 3074, 96368) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5407, 3074, 96368 is 1.
Step 1: Since 5407 > 3074, we apply the division lemma to 5407 and 3074, to get
5407 = 3074 x 1 + 2333
Step 2: Since the reminder 3074 ≠ 0, we apply division lemma to 2333 and 3074, to get
3074 = 2333 x 1 + 741
Step 3: We consider the new divisor 2333 and the new remainder 741, and apply the division lemma to get
2333 = 741 x 3 + 110
We consider the new divisor 741 and the new remainder 110,and apply the division lemma to get
741 = 110 x 6 + 81
We consider the new divisor 110 and the new remainder 81,and apply the division lemma to get
110 = 81 x 1 + 29
We consider the new divisor 81 and the new remainder 29,and apply the division lemma to get
81 = 29 x 2 + 23
We consider the new divisor 29 and the new remainder 23,and apply the division lemma to get
29 = 23 x 1 + 6
We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get
23 = 6 x 3 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5407 and 3074 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(29,23) = HCF(81,29) = HCF(110,81) = HCF(741,110) = HCF(2333,741) = HCF(3074,2333) = HCF(5407,3074) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 96368 > 1, we apply the division lemma to 96368 and 1, to get
96368 = 1 x 96368 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 96368 is 1
Notice that 1 = HCF(96368,1) .
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 5407, 3074, 96368?
Answer: HCF of 5407, 3074, 96368 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5407, 3074, 96368 using Euclid's Algorithm?
Answer: For arbitrary numbers 5407, 3074, 96368 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.