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 878, 540, 82 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 878, 540, 82 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 878, 540, 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 878, 540, 82 is 2.
HCF(878, 540, 82) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 878, 540, 82 is 2.
Step 1: Since 878 > 540, we apply the division lemma to 878 and 540, to get
878 = 540 x 1 + 338
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 338 and 540, to get
540 = 338 x 1 + 202
Step 3: We consider the new divisor 338 and the new remainder 202, and apply the division lemma to get
338 = 202 x 1 + 136
We consider the new divisor 202 and the new remainder 136,and apply the division lemma to get
202 = 136 x 1 + 66
We consider the new divisor 136 and the new remainder 66,and apply the division lemma to get
136 = 66 x 2 + 4
We consider the new divisor 66 and the new remainder 4,and apply the division lemma to get
66 = 4 x 16 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 878 and 540 is 2
Notice that 2 = HCF(4,2) = HCF(66,4) = HCF(136,66) = HCF(202,136) = HCF(338,202) = HCF(540,338) = HCF(878,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 2, we apply the division lemma to 82 and 2, to get
82 = 2 x 41 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 82 is 2
Notice that 2 = HCF(82,2) .
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 878, 540, 82?
Answer: HCF of 878, 540, 82 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 878, 540, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 878, 540, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.