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 362, 622, 204 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 362, 622, 204 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 362, 622, 204 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 362, 622, 204 is 2.
HCF(362, 622, 204) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 362, 622, 204 is 2.
Step 1: Since 622 > 362, we apply the division lemma to 622 and 362, to get
622 = 362 x 1 + 260
Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 260 and 362, to get
362 = 260 x 1 + 102
Step 3: We consider the new divisor 260 and the new remainder 102, and apply the division lemma to get
260 = 102 x 2 + 56
We consider the new divisor 102 and the new remainder 56,and apply the division lemma to get
102 = 56 x 1 + 46
We consider the new divisor 56 and the new remainder 46,and apply the division lemma to get
56 = 46 x 1 + 10
We consider the new divisor 46 and the new remainder 10,and apply the division lemma to get
46 = 10 x 4 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 362 and 622 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(46,10) = HCF(56,46) = HCF(102,56) = HCF(260,102) = HCF(362,260) = HCF(622,362) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 204 > 2, we apply the division lemma to 204 and 2, to get
204 = 2 x 102 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 204 is 2
Notice that 2 = HCF(204,2) .
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 362, 622, 204?
Answer: HCF of 362, 622, 204 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 362, 622, 204 using Euclid's Algorithm?
Answer: For arbitrary numbers 362, 622, 204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.