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 2352, 4474, 82239 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2352, 4474, 82239 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 2352, 4474, 82239 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 2352, 4474, 82239 is 1.
HCF(2352, 4474, 82239) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2352, 4474, 82239 is 1.
Step 1: Since 4474 > 2352, we apply the division lemma to 4474 and 2352, to get
4474 = 2352 x 1 + 2122
Step 2: Since the reminder 2352 ≠ 0, we apply division lemma to 2122 and 2352, to get
2352 = 2122 x 1 + 230
Step 3: We consider the new divisor 2122 and the new remainder 230, and apply the division lemma to get
2122 = 230 x 9 + 52
We consider the new divisor 230 and the new remainder 52,and apply the division lemma to get
230 = 52 x 4 + 22
We consider the new divisor 52 and the new remainder 22,and apply the division lemma to get
52 = 22 x 2 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2352 and 4474 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(52,22) = HCF(230,52) = HCF(2122,230) = HCF(2352,2122) = HCF(4474,2352) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82239 > 2, we apply the division lemma to 82239 and 2, to get
82239 = 2 x 41119 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 82239 is 1
Notice that 1 = HCF(2,1) = HCF(82239,2) .
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 2352, 4474, 82239?
Answer: HCF of 2352, 4474, 82239 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2352, 4474, 82239 using Euclid's Algorithm?
Answer: For arbitrary numbers 2352, 4474, 82239 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.