Highest Common Factor of 532, 420 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 532, 420 i.e. 28 the largest integer that leaves a remainder zero for all numbers.
HCF of 532, 420 is 28 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 532, 420 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 532, 420 is 28.
HCF(532, 420) = 28
HCF of 532, 420 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 532, 420 is 28.
Highest Common Factor of 532,420 is 28
Step 1: Since 532 > 420, we apply the division lemma to 532 and 420, to get
532 = 420 x 1 + 112
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 112 and 420, to get
420 = 112 x 3 + 84
Step 3: We consider the new divisor 112 and the new remainder 84, and apply the division lemma to get
112 = 84 x 1 + 28
We consider the new divisor 84 and the new remainder 28, and apply the division lemma to get
84 = 28 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 532 and 420 is 28
Notice that 28 = HCF(84,28) = HCF(112,84) = HCF(420,112) = HCF(532,420) .
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Frequently Asked Questions on HCF of 532, 420 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 532, 420?
Answer: HCF of 532, 420 is 28 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 532, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 532, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.