Highest Common Factor of 585, 921, 900 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 585, 921, 900 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 585, 921, 900 is 3 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 585, 921, 900 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 585, 921, 900 is 3.
HCF(585, 921, 900) = 3
HCF of 585, 921, 900 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 585, 921, 900 is 3.
Highest Common Factor of 585,921,900 is 3
Step 1: Since 921 > 585, we apply the division lemma to 921 and 585, to get
921 = 585 x 1 + 336
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 336 and 585, to get
585 = 336 x 1 + 249
Step 3: We consider the new divisor 336 and the new remainder 249, and apply the division lemma to get
336 = 249 x 1 + 87
We consider the new divisor 249 and the new remainder 87,and apply the division lemma to get
249 = 87 x 2 + 75
We consider the new divisor 87 and the new remainder 75,and apply the division lemma to get
87 = 75 x 1 + 12
We consider the new divisor 75 and the new remainder 12,and apply the division lemma to get
75 = 12 x 6 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 585 and 921 is 3
Notice that 3 = HCF(12,3) = HCF(75,12) = HCF(87,75) = HCF(249,87) = HCF(336,249) = HCF(585,336) = HCF(921,585) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 900 > 3, we apply the division lemma to 900 and 3, to get
900 = 3 x 300 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 900 is 3
Notice that 3 = HCF(900,3) .
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Frequently Asked Questions on HCF of 585, 921, 900 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 585, 921, 900?
Answer: HCF of 585, 921, 900 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 585, 921, 900 using Euclid's Algorithm?
Answer: For arbitrary numbers 585, 921, 900 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.