Highest Common Factor of 420, 723 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 420, 723 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 723 is 3 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 420, 723 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 420, 723 is 3.
HCF(420, 723) = 3
HCF of 420, 723 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 723 is 3.
Highest Common Factor of 420,723 is 3
Step 1: Since 723 > 420, we apply the division lemma to 723 and 420, to get
723 = 420 x 1 + 303
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 303 and 420, to get
420 = 303 x 1 + 117
Step 3: We consider the new divisor 303 and the new remainder 117, and apply the division lemma to get
303 = 117 x 2 + 69
We consider the new divisor 117 and the new remainder 69,and apply the division lemma to get
117 = 69 x 1 + 48
We consider the new divisor 69 and the new remainder 48,and apply the division lemma to get
69 = 48 x 1 + 21
We consider the new divisor 48 and the new remainder 21,and apply the division lemma to get
48 = 21 x 2 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 420 and 723 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(48,21) = HCF(69,48) = HCF(117,69) = HCF(303,117) = HCF(420,303) = HCF(723,420) .
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Frequently Asked Questions on HCF of 420, 723 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 420, 723?
Answer: HCF of 420, 723 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 723 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.