Highest Common Factor of 540, 740, 999 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, 740, 999 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 540, 740, 999 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, 740, 999 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, 740, 999 is 1.
HCF(540, 740, 999) = 1
HCF of 540, 740, 999 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, 740, 999 is 1.
Highest Common Factor of 540,740,999 is 1
Step 1: Since 740 > 540, we apply the division lemma to 740 and 540, to get
740 = 540 x 1 + 200
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 200 and 540, to get
540 = 200 x 2 + 140
Step 3: We consider the new divisor 200 and the new remainder 140, and apply the division lemma to get
200 = 140 x 1 + 60
We consider the new divisor 140 and the new remainder 60,and apply the division lemma to get
140 = 60 x 2 + 20
We consider the new divisor 60 and the new remainder 20,and apply the division lemma to get
60 = 20 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 540 and 740 is 20
Notice that 20 = HCF(60,20) = HCF(140,60) = HCF(200,140) = HCF(540,200) = HCF(740,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 999 > 20, we apply the division lemma to 999 and 20, to get
999 = 20 x 49 + 19
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 19 and 20, to get
20 = 19 x 1 + 1
Step 3: We consider the new divisor 19 and the new remainder 1, and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 20 and 999 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(999,20) .
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Frequently Asked Questions on HCF of 540, 740, 999 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, 740, 999?
Answer: HCF of 540, 740, 999 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 540, 740, 999 using Euclid's Algorithm?
Answer: For arbitrary numbers 540, 740, 999 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.