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 512, 111, 862, 103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 512, 111, 862, 103 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 512, 111, 862, 103 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 512, 111, 862, 103 is 1.
HCF(512, 111, 862, 103) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 512, 111, 862, 103 is 1.
Step 1: Since 512 > 111, we apply the division lemma to 512 and 111, to get
512 = 111 x 4 + 68
Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 68 and 111, to get
111 = 68 x 1 + 43
Step 3: We consider the new divisor 68 and the new remainder 43, and apply the division lemma to get
68 = 43 x 1 + 25
We consider the new divisor 43 and the new remainder 25,and apply the division lemma to get
43 = 25 x 1 + 18
We consider the new divisor 25 and the new remainder 18,and apply the division lemma to get
25 = 18 x 1 + 7
We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get
18 = 7 x 2 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 512 and 111 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(25,18) = HCF(43,25) = HCF(68,43) = HCF(111,68) = HCF(512,111) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 862 > 1, we apply the division lemma to 862 and 1, to get
862 = 1 x 862 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 862 is 1
Notice that 1 = HCF(862,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 103 > 1, we apply the division lemma to 103 and 1, to get
103 = 1 x 103 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 103 is 1
Notice that 1 = HCF(103,1) .
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 512, 111, 862, 103?
Answer: HCF of 512, 111, 862, 103 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 512, 111, 862, 103 using Euclid's Algorithm?
Answer: For arbitrary numbers 512, 111, 862, 103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.