Highest Common Factor of 742, 1592, 9412 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 742, 1592, 9412 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 1592, 9412 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 742, 1592, 9412 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 742, 1592, 9412 is 2.
HCF(742, 1592, 9412) = 2
HCF of 742, 1592, 9412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 742, 1592, 9412 is 2.
Highest Common Factor of 742,1592,9412 is 2
Step 1: Since 1592 > 742, we apply the division lemma to 1592 and 742, to get
1592 = 742 x 2 + 108
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 108 and 742, to get
742 = 108 x 6 + 94
Step 3: We consider the new divisor 108 and the new remainder 94, and apply the division lemma to get
108 = 94 x 1 + 14
We consider the new divisor 94 and the new remainder 14,and apply the division lemma to get
94 = 14 x 6 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 742 and 1592 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(94,14) = HCF(108,94) = HCF(742,108) = HCF(1592,742) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9412 > 2, we apply the division lemma to 9412 and 2, to get
9412 = 2 x 4706 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9412 is 2
Notice that 2 = HCF(9412,2) .
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Frequently Asked Questions on HCF of 742, 1592, 9412 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 742, 1592, 9412?
Answer: HCF of 742, 1592, 9412 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 1592, 9412 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 1592, 9412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.