Highest Common Factor of 1800, 472 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 1800, 472 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 1800, 472 is 8 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 1800, 472 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 1800, 472 is 8.
HCF(1800, 472) = 8
HCF of 1800, 472 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1800, 472 is 8.
Highest Common Factor of 1800,472 is 8
Step 1: Since 1800 > 472, we apply the division lemma to 1800 and 472, to get
1800 = 472 x 3 + 384
Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 384 and 472, to get
472 = 384 x 1 + 88
Step 3: We consider the new divisor 384 and the new remainder 88, and apply the division lemma to get
384 = 88 x 4 + 32
We consider the new divisor 88 and the new remainder 32,and apply the division lemma to get
88 = 32 x 2 + 24
We consider the new divisor 32 and the new remainder 24,and apply the division lemma to get
32 = 24 x 1 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 1800 and 472 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(88,32) = HCF(384,88) = HCF(472,384) = HCF(1800,472) .
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Frequently Asked Questions on HCF of 1800, 472 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 1800, 472?
Answer: HCF of 1800, 472 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1800, 472 using Euclid's Algorithm?
Answer: For arbitrary numbers 1800, 472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
