Highest Common Factor of 198, 968, 46 using Euclid's algorithm
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 198, 968, 46 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 198, 968, 46 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 198, 968, 46 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 198, 968, 46 is 2.
HCF(198, 968, 46) = 2
HCF of 198, 968, 46 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 198, 968, 46 is 2.
Highest Common Factor of 198,968,46 is 2
Step 1: Since 968 > 198, we apply the division lemma to 968 and 198, to get
968 = 198 x 4 + 176
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 176 and 198, to get
198 = 176 x 1 + 22
Step 3: We consider the new divisor 176 and the new remainder 22, and apply the division lemma to get
176 = 22 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 198 and 968 is 22
Notice that 22 = HCF(176,22) = HCF(198,176) = HCF(968,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 46 > 22, we apply the division lemma to 46 and 22, to get
46 = 22 x 2 + 2
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 2 and 22, to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 22 and 46 is 2
Notice that 2 = HCF(22,2) = HCF(46,22) .
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Frequently Asked Questions on HCF of 198, 968, 46 using Euclid's Algorithm
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 198, 968, 46?
Answer: HCF of 198, 968, 46 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 198, 968, 46 using Euclid's Algorithm?
Answer: For arbitrary numbers 198, 968, 46 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.