Highest Common Factor of 900, 16540 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 900, 16540 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 16540 is 20 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 900, 16540 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 900, 16540 is 20.
HCF(900, 16540) = 20
HCF of 900, 16540 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 16540 is 20.
Highest Common Factor of 900,16540 is 20
Step 1: Since 16540 > 900, we apply the division lemma to 16540 and 900, to get
16540 = 900 x 18 + 340
Step 2: Since the reminder 900 ≠ 0, we apply division lemma to 340 and 900, to get
900 = 340 x 2 + 220
Step 3: We consider the new divisor 340 and the new remainder 220, and apply the division lemma to get
340 = 220 x 1 + 120
We consider the new divisor 220 and the new remainder 120,and apply the division lemma to get
220 = 120 x 1 + 100
We consider the new divisor 120 and the new remainder 100,and apply the division lemma to get
120 = 100 x 1 + 20
We consider the new divisor 100 and the new remainder 20,and apply the division lemma to get
100 = 20 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 900 and 16540 is 20
Notice that 20 = HCF(100,20) = HCF(120,100) = HCF(220,120) = HCF(340,220) = HCF(900,340) = HCF(16540,900) .
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Frequently Asked Questions on HCF of 900, 16540 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 900, 16540?
Answer: HCF of 900, 16540 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 16540 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 16540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.