Highest Common Factor of 423, 1528 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, 1528 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 1528 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, 1528 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, 1528 is 1.
HCF(423, 1528) = 1
HCF of 423, 1528 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, 1528 is 1.
Highest Common Factor of 423,1528 is 1
Step 1: Since 1528 > 423, we apply the division lemma to 1528 and 423, to get
1528 = 423 x 3 + 259
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 259 and 423, to get
423 = 259 x 1 + 164
Step 3: We consider the new divisor 259 and the new remainder 164, and apply the division lemma to get
259 = 164 x 1 + 95
We consider the new divisor 164 and the new remainder 95,and apply the division lemma to get
164 = 95 x 1 + 69
We consider the new divisor 95 and the new remainder 69,and apply the division lemma to get
95 = 69 x 1 + 26
We consider the new divisor 69 and the new remainder 26,and apply the division lemma to get
69 = 26 x 2 + 17
We consider the new divisor 26 and the new remainder 17,and apply the division lemma to get
26 = 17 x 1 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 423 and 1528 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(26,17) = HCF(69,26) = HCF(95,69) = HCF(164,95) = HCF(259,164) = HCF(423,259) = HCF(1528,423) .
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Frequently Asked Questions on HCF of 423, 1528 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, 1528?
Answer: HCF of 423, 1528 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 1528 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 1528 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.