Highest Common Factor of 461, 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 461, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 461, 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 461, 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 461, 749 is 1.
HCF(461, 749) = 1
HCF of 461, 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 461, 749 is 1.
Highest Common Factor of 461,749 is 1
Step 1: Since 749 > 461, we apply the division lemma to 749 and 461, to get
749 = 461 x 1 + 288
Step 2: Since the reminder 461 ≠ 0, we apply division lemma to 288 and 461, to get
461 = 288 x 1 + 173
Step 3: We consider the new divisor 288 and the new remainder 173, and apply the division lemma to get
288 = 173 x 1 + 115
We consider the new divisor 173 and the new remainder 115,and apply the division lemma to get
173 = 115 x 1 + 58
We consider the new divisor 115 and the new remainder 58,and apply the division lemma to get
115 = 58 x 1 + 57
We consider the new divisor 58 and the new remainder 57,and apply the division lemma to get
58 = 57 x 1 + 1
We consider the new divisor 57 and the new remainder 1,and apply the division lemma to get
57 = 1 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 461 and 749 is 1
Notice that 1 = HCF(57,1) = HCF(58,57) = HCF(115,58) = HCF(173,115) = HCF(288,173) = HCF(461,288) = HCF(749,461) .
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Frequently Asked Questions on HCF of 461, 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 461, 749?
Answer: HCF of 461, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 461, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 461, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.