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 830, 675, 519, 82 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 830, 675, 519, 82 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 830, 675, 519, 82 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 830, 675, 519, 82 is 1.
HCF(830, 675, 519, 82) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 830, 675, 519, 82 is 1.
Step 1: Since 830 > 675, we apply the division lemma to 830 and 675, to get
830 = 675 x 1 + 155
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 155 and 675, to get
675 = 155 x 4 + 55
Step 3: We consider the new divisor 155 and the new remainder 55, and apply the division lemma to get
155 = 55 x 2 + 45
We consider the new divisor 55 and the new remainder 45,and apply the division lemma to get
55 = 45 x 1 + 10
We consider the new divisor 45 and the new remainder 10,and apply the division lemma to get
45 = 10 x 4 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 830 and 675 is 5
Notice that 5 = HCF(10,5) = HCF(45,10) = HCF(55,45) = HCF(155,55) = HCF(675,155) = HCF(830,675) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 519 > 5, we apply the division lemma to 519 and 5, to get
519 = 5 x 103 + 4
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get
5 = 4 x 1 + 1
Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 519 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(519,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 1, we apply the division lemma to 82 and 1, to get
82 = 1 x 82 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 82 is 1
Notice that 1 = HCF(82,1) .
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 830, 675, 519, 82?
Answer: HCF of 830, 675, 519, 82 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 830, 675, 519, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 830, 675, 519, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.