Highest Common Factor of 423, 690, 220 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 423, 690, 220 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 690, 220 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 423, 690, 220 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 423, 690, 220 is 1.
HCF(423, 690, 220) = 1
HCF of 423, 690, 220 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 423, 690, 220 is 1.
Highest Common Factor of 423,690,220 is 1
Step 1: Since 690 > 423, we apply the division lemma to 690 and 423, to get
690 = 423 x 1 + 267
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 267 and 423, to get
423 = 267 x 1 + 156
Step 3: We consider the new divisor 267 and the new remainder 156, and apply the division lemma to get
267 = 156 x 1 + 111
We consider the new divisor 156 and the new remainder 111,and apply the division lemma to get
156 = 111 x 1 + 45
We consider the new divisor 111 and the new remainder 45,and apply the division lemma to get
111 = 45 x 2 + 21
We consider the new divisor 45 and the new remainder 21,and apply the division lemma to get
45 = 21 x 2 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 423 and 690 is 3
Notice that 3 = HCF(21,3) = HCF(45,21) = HCF(111,45) = HCF(156,111) = HCF(267,156) = HCF(423,267) = HCF(690,423) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 220 > 3, we apply the division lemma to 220 and 3, to get
220 = 3 x 73 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 220 is 1
Notice that 1 = HCF(3,1) = HCF(220,3) .
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Frequently Asked Questions on HCF of 423, 690, 220 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 423, 690, 220?
Answer: HCF of 423, 690, 220 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 690, 220 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 690, 220 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.