Highest Common Factor of 198, 726, 158 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, 726, 158 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 198, 726, 158 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, 726, 158 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, 726, 158 is 2.
HCF(198, 726, 158) = 2
HCF of 198, 726, 158 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, 726, 158 is 2.
Highest Common Factor of 198,726,158 is 2
Step 1: Since 726 > 198, we apply the division lemma to 726 and 198, to get
726 = 198 x 3 + 132
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 132 and 198, to get
198 = 132 x 1 + 66
Step 3: We consider the new divisor 132 and the new remainder 66, and apply the division lemma to get
132 = 66 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 66, the HCF of 198 and 726 is 66
Notice that 66 = HCF(132,66) = HCF(198,132) = HCF(726,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 158 > 66, we apply the division lemma to 158 and 66, to get
158 = 66 x 2 + 26
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 26 and 66, to get
66 = 26 x 2 + 14
Step 3: We consider the new divisor 26 and the new remainder 14, and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 66 and 158 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(66,26) = HCF(158,66) .
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Frequently Asked Questions on HCF of 198, 726, 158 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, 726, 158?
Answer: HCF of 198, 726, 158 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 198, 726, 158 using Euclid's Algorithm?
Answer: For arbitrary numbers 198, 726, 158 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
