Highest Common Factor of 540, 972, 583 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 540, 972, 583 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 540, 972, 583 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 540, 972, 583 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 540, 972, 583 is 1.
HCF(540, 972, 583) = 1
HCF of 540, 972, 583 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 540, 972, 583 is 1.
Highest Common Factor of 540,972,583 is 1
Step 1: Since 972 > 540, we apply the division lemma to 972 and 540, to get
972 = 540 x 1 + 432
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 432 and 540, to get
540 = 432 x 1 + 108
Step 3: We consider the new divisor 432 and the new remainder 108, and apply the division lemma to get
432 = 108 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 108, the HCF of 540 and 972 is 108
Notice that 108 = HCF(432,108) = HCF(540,432) = HCF(972,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 583 > 108, we apply the division lemma to 583 and 108, to get
583 = 108 x 5 + 43
Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 43 and 108, to get
108 = 43 x 2 + 22
Step 3: We consider the new divisor 43 and the new remainder 22, and apply the division lemma to get
43 = 22 x 1 + 21
We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get
22 = 21 x 1 + 1
We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 108 and 583 is 1
Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(43,22) = HCF(108,43) = HCF(583,108) .
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Frequently Asked Questions on HCF of 540, 972, 583 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 540, 972, 583?
Answer: HCF of 540, 972, 583 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 540, 972, 583 using Euclid's Algorithm?
Answer: For arbitrary numbers 540, 972, 583 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.