Highest Common Factor of 464, 7128, 2826 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 464, 7128, 2826 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 464, 7128, 2826 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 464, 7128, 2826 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 464, 7128, 2826 is 2.
HCF(464, 7128, 2826) = 2
HCF of 464, 7128, 2826 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 464, 7128, 2826 is 2.
Highest Common Factor of 464,7128,2826 is 2
Step 1: Since 7128 > 464, we apply the division lemma to 7128 and 464, to get
7128 = 464 x 15 + 168
Step 2: Since the reminder 464 ≠ 0, we apply division lemma to 168 and 464, to get
464 = 168 x 2 + 128
Step 3: We consider the new divisor 168 and the new remainder 128, and apply the division lemma to get
168 = 128 x 1 + 40
We consider the new divisor 128 and the new remainder 40,and apply the division lemma to get
128 = 40 x 3 + 8
We consider the new divisor 40 and the new remainder 8,and apply the division lemma to get
40 = 8 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 464 and 7128 is 8
Notice that 8 = HCF(40,8) = HCF(128,40) = HCF(168,128) = HCF(464,168) = HCF(7128,464) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2826 > 8, we apply the division lemma to 2826 and 8, to get
2826 = 8 x 353 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, 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 8 and 2826 is 2
Notice that 2 = HCF(8,2) = HCF(2826,8) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 464, 7128, 2826 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 464, 7128, 2826?
Answer: HCF of 464, 7128, 2826 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 464, 7128, 2826 using Euclid's Algorithm?
Answer: For arbitrary numbers 464, 7128, 2826 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.