Highest Common Factor of 460, 667, 540 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 460, 667, 540 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 667, 540 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 460, 667, 540 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 460, 667, 540 is 1.
HCF(460, 667, 540) = 1
HCF of 460, 667, 540 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 667, 540 is 1.
Highest Common Factor of 460,667,540 is 1
Step 1: Since 667 > 460, we apply the division lemma to 667 and 460, to get
667 = 460 x 1 + 207
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 207 and 460, to get
460 = 207 x 2 + 46
Step 3: We consider the new divisor 207 and the new remainder 46, and apply the division lemma to get
207 = 46 x 4 + 23
We consider the new divisor 46 and the new remainder 23, and apply the division lemma to get
46 = 23 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 460 and 667 is 23
Notice that 23 = HCF(46,23) = HCF(207,46) = HCF(460,207) = HCF(667,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 540 > 23, we apply the division lemma to 540 and 23, to get
540 = 23 x 23 + 11
Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 11 and 23, to get
23 = 11 x 2 + 1
Step 3: We consider the new divisor 11 and the new remainder 1, and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 23 and 540 is 1
Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(540,23) .
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Frequently Asked Questions on HCF of 460, 667, 540 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 460, 667, 540?
Answer: HCF of 460, 667, 540 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 667, 540 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 667, 540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.