Highest Common Factor of 738, 542, 162 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 738, 542, 162 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 738, 542, 162 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 738, 542, 162 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 738, 542, 162 is 2.
HCF(738, 542, 162) = 2
HCF of 738, 542, 162 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 738, 542, 162 is 2.
Highest Common Factor of 738,542,162 is 2
Step 1: Since 738 > 542, we apply the division lemma to 738 and 542, to get
738 = 542 x 1 + 196
Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 196 and 542, to get
542 = 196 x 2 + 150
Step 3: We consider the new divisor 196 and the new remainder 150, and apply the division lemma to get
196 = 150 x 1 + 46
We consider the new divisor 150 and the new remainder 46,and apply the division lemma to get
150 = 46 x 3 + 12
We consider the new divisor 46 and the new remainder 12,and apply the division lemma to get
46 = 12 x 3 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 738 and 542 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(46,12) = HCF(150,46) = HCF(196,150) = HCF(542,196) = HCF(738,542) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 162 > 2, we apply the division lemma to 162 and 2, to get
162 = 2 x 81 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 162 is 2
Notice that 2 = HCF(162,2) .
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Frequently Asked Questions on HCF of 738, 542, 162 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 738, 542, 162?
Answer: HCF of 738, 542, 162 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 738, 542, 162 using Euclid's Algorithm?
Answer: For arbitrary numbers 738, 542, 162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.