Highest Common Factor of 540, 702, 406 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, 702, 406 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 540, 702, 406 is 2 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, 702, 406 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, 702, 406 is 2.
HCF(540, 702, 406) = 2
HCF of 540, 702, 406 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, 702, 406 is 2.
Highest Common Factor of 540,702,406 is 2
Step 1: Since 702 > 540, we apply the division lemma to 702 and 540, to get
702 = 540 x 1 + 162
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 162 and 540, to get
540 = 162 x 3 + 54
Step 3: We consider the new divisor 162 and the new remainder 54, and apply the division lemma to get
162 = 54 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 540 and 702 is 54
Notice that 54 = HCF(162,54) = HCF(540,162) = HCF(702,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 406 > 54, we apply the division lemma to 406 and 54, to get
406 = 54 x 7 + 28
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 28 and 54, to get
54 = 28 x 1 + 26
Step 3: We consider the new divisor 28 and the new remainder 26, and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2, and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 54 and 406 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(54,28) = HCF(406,54) .
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Frequently Asked Questions on HCF of 540, 702, 406 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, 702, 406?
Answer: HCF of 540, 702, 406 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 540, 702, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 540, 702, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.