Highest Common Factor of 900, 351, 477 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, 351, 477 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 351, 477 is 9 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, 351, 477 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, 351, 477 is 9.
HCF(900, 351, 477) = 9
HCF of 900, 351, 477 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, 351, 477 is 9.
Highest Common Factor of 900,351,477 is 9
Step 1: Since 900 > 351, we apply the division lemma to 900 and 351, to get
900 = 351 x 2 + 198
Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 198 and 351, to get
351 = 198 x 1 + 153
Step 3: We consider the new divisor 198 and the new remainder 153, and apply the division lemma to get
198 = 153 x 1 + 45
We consider the new divisor 153 and the new remainder 45,and apply the division lemma to get
153 = 45 x 3 + 18
We consider the new divisor 45 and the new remainder 18,and apply the division lemma to get
45 = 18 x 2 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 900 and 351 is 9
Notice that 9 = HCF(18,9) = HCF(45,18) = HCF(153,45) = HCF(198,153) = HCF(351,198) = HCF(900,351) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 477 > 9, we apply the division lemma to 477 and 9, to get
477 = 9 x 53 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 477 is 9
Notice that 9 = HCF(477,9) .
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Frequently Asked Questions on HCF of 900, 351, 477 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, 351, 477?
Answer: HCF of 900, 351, 477 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 351, 477 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 351, 477 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.