Highest Common Factor of 465, 749 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 465, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 465, 749 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 465, 749 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 465, 749 is 1.
HCF(465, 749) = 1
HCF of 465, 749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 465, 749 is 1.
Highest Common Factor of 465,749 is 1
Step 1: Since 749 > 465, we apply the division lemma to 749 and 465, to get
749 = 465 x 1 + 284
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 284 and 465, to get
465 = 284 x 1 + 181
Step 3: We consider the new divisor 284 and the new remainder 181, and apply the division lemma to get
284 = 181 x 1 + 103
We consider the new divisor 181 and the new remainder 103,and apply the division lemma to get
181 = 103 x 1 + 78
We consider the new divisor 103 and the new remainder 78,and apply the division lemma to get
103 = 78 x 1 + 25
We consider the new divisor 78 and the new remainder 25,and apply the division lemma to get
78 = 25 x 3 + 3
We consider the new divisor 25 and the new remainder 3,and apply the division lemma to get
25 = 3 x 8 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 465 and 749 is 1
Notice that 1 = HCF(3,1) = HCF(25,3) = HCF(78,25) = HCF(103,78) = HCF(181,103) = HCF(284,181) = HCF(465,284) = HCF(749,465) .
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Frequently Asked Questions on HCF of 465, 749 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 465, 749?
Answer: HCF of 465, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 465, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 465, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.