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 996, 166, 198 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 166, 198 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 996, 166, 198 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 996, 166, 198 is 2.
HCF(996, 166, 198) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 996, 166, 198 is 2.
Step 1: Since 996 > 166, we apply the division lemma to 996 and 166, to get
996 = 166 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 166, the HCF of 996 and 166 is 166
Notice that 166 = HCF(996,166) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 198 > 166, we apply the division lemma to 198 and 166, to get
198 = 166 x 1 + 32
Step 2: Since the reminder 166 ≠ 0, we apply division lemma to 32 and 166, to get
166 = 32 x 5 + 6
Step 3: We consider the new divisor 32 and the new remainder 6, and apply the division lemma to get
32 = 6 x 5 + 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 166 and 198 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(166,32) = HCF(198,166) .
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 996, 166, 198?
Answer: HCF of 996, 166, 198 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 166, 198 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 166, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.