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 457, 3108, 5758 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 457, 3108, 5758 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 457, 3108, 5758 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 457, 3108, 5758 is 1.
HCF(457, 3108, 5758) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 457, 3108, 5758 is 1.
Step 1: Since 3108 > 457, we apply the division lemma to 3108 and 457, to get
3108 = 457 x 6 + 366
Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 366 and 457, to get
457 = 366 x 1 + 91
Step 3: We consider the new divisor 366 and the new remainder 91, and apply the division lemma to get
366 = 91 x 4 + 2
We consider the new divisor 91 and the new remainder 2,and apply the division lemma to get
91 = 2 x 45 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 3108 is 1
Notice that 1 = HCF(2,1) = HCF(91,2) = HCF(366,91) = HCF(457,366) = HCF(3108,457) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5758 > 1, we apply the division lemma to 5758 and 1, to get
5758 = 1 x 5758 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5758 is 1
Notice that 1 = HCF(5758,1) .
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 457, 3108, 5758?
Answer: HCF of 457, 3108, 5758 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 457, 3108, 5758 using Euclid's Algorithm?
Answer: For arbitrary numbers 457, 3108, 5758 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.