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, 983, 174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 362, 983, 174 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 362, 983, 174 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, 983, 174 is 1.
HCF(362, 983, 174) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 362, 983, 174 is 1.
Step 1: Since 983 > 362, we apply the division lemma to 983 and 362, to get
983 = 362 x 2 + 259
Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 259 and 362, to get
362 = 259 x 1 + 103
Step 3: We consider the new divisor 259 and the new remainder 103, and apply the division lemma to get
259 = 103 x 2 + 53
We consider the new divisor 103 and the new remainder 53,and apply the division lemma to get
103 = 53 x 1 + 50
We consider the new divisor 53 and the new remainder 50,and apply the division lemma to get
53 = 50 x 1 + 3
We consider the new divisor 50 and the new remainder 3,and apply the division lemma to get
50 = 3 x 16 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 362 and 983 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(50,3) = HCF(53,50) = HCF(103,53) = HCF(259,103) = HCF(362,259) = HCF(983,362) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 174 > 1, we apply the division lemma to 174 and 1, to get
174 = 1 x 174 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 174 is 1
Notice that 1 = HCF(174,1) .
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 362, 983, 174?
Answer: HCF of 362, 983, 174 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 362, 983, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 362, 983, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.