Highest Common Factor of 546, 702, 365, 21 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 546, 702, 365, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 702, 365, 21 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 546, 702, 365, 21 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 546, 702, 365, 21 is 1.
HCF(546, 702, 365, 21) = 1
HCF of 546, 702, 365, 21 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 546, 702, 365, 21 is 1.
Highest Common Factor of 546,702,365,21 is 1
Step 1: Since 702 > 546, we apply the division lemma to 702 and 546, to get
702 = 546 x 1 + 156
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 156 and 546, to get
546 = 156 x 3 + 78
Step 3: We consider the new divisor 156 and the new remainder 78, and apply the division lemma to get
156 = 78 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 78, the HCF of 546 and 702 is 78
Notice that 78 = HCF(156,78) = HCF(546,156) = HCF(702,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 365 > 78, we apply the division lemma to 365 and 78, to get
365 = 78 x 4 + 53
Step 2: Since the reminder 78 ≠ 0, we apply division lemma to 53 and 78, to get
78 = 53 x 1 + 25
Step 3: We consider the new divisor 53 and the new remainder 25, and apply the division lemma to get
53 = 25 x 2 + 3
We consider the new divisor 25 and the new remainder 3,and apply the division lemma to get
25 = 3 x 8 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 78 and 365 is 1
Notice that 1 = HCF(3,1) = HCF(25,3) = HCF(53,25) = HCF(78,53) = HCF(365,78) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, 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 1 and 21 is 1
Notice that 1 = HCF(21,1) .
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Frequently Asked Questions on HCF of 546, 702, 365, 21 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 546, 702, 365, 21?
Answer: HCF of 546, 702, 365, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 702, 365, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 702, 365, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.