Highest Common Factor of 742, 9460, 6762 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, 9460, 6762 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 9460, 6762 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, 9460, 6762 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, 9460, 6762 is 2.
HCF(742, 9460, 6762) = 2
HCF of 742, 9460, 6762 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, 9460, 6762 is 2.
Highest Common Factor of 742,9460,6762 is 2
Step 1: Since 9460 > 742, we apply the division lemma to 9460 and 742, to get
9460 = 742 x 12 + 556
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 556 and 742, to get
742 = 556 x 1 + 186
Step 3: We consider the new divisor 556 and the new remainder 186, and apply the division lemma to get
556 = 186 x 2 + 184
We consider the new divisor 186 and the new remainder 184,and apply the division lemma to get
186 = 184 x 1 + 2
We consider the new divisor 184 and the new remainder 2,and apply the division lemma to get
184 = 2 x 92 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 742 and 9460 is 2
Notice that 2 = HCF(184,2) = HCF(186,184) = HCF(556,186) = HCF(742,556) = HCF(9460,742) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6762 > 2, we apply the division lemma to 6762 and 2, to get
6762 = 2 x 3381 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 6762 is 2
Notice that 2 = HCF(6762,2) .
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Frequently Asked Questions on HCF of 742, 9460, 6762 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, 9460, 6762?
Answer: HCF of 742, 9460, 6762 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 9460, 6762 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 9460, 6762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
