Highest Common Factor of 742, 5735 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, 5735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 5735 is 1 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, 5735 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, 5735 is 1.
HCF(742, 5735) = 1
HCF of 742, 5735 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, 5735 is 1.
Highest Common Factor of 742,5735 is 1
Step 1: Since 5735 > 742, we apply the division lemma to 5735 and 742, to get
5735 = 742 x 7 + 541
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 541 and 742, to get
742 = 541 x 1 + 201
Step 3: We consider the new divisor 541 and the new remainder 201, and apply the division lemma to get
541 = 201 x 2 + 139
We consider the new divisor 201 and the new remainder 139,and apply the division lemma to get
201 = 139 x 1 + 62
We consider the new divisor 139 and the new remainder 62,and apply the division lemma to get
139 = 62 x 2 + 15
We consider the new divisor 62 and the new remainder 15,and apply the division lemma to get
62 = 15 x 4 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 742 and 5735 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(62,15) = HCF(139,62) = HCF(201,139) = HCF(541,201) = HCF(742,541) = HCF(5735,742) .
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Frequently Asked Questions on HCF of 742, 5735 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, 5735?
Answer: HCF of 742, 5735 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 5735 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 5735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.