Highest Common Factor of 435, 600, 261 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 435, 600, 261 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 435, 600, 261 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 435, 600, 261 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 435, 600, 261 is 3.
HCF(435, 600, 261) = 3
HCF of 435, 600, 261 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 435, 600, 261 is 3.
Highest Common Factor of 435,600,261 is 3
Step 1: Since 600 > 435, we apply the division lemma to 600 and 435, to get
600 = 435 x 1 + 165
Step 2: Since the reminder 435 ≠ 0, we apply division lemma to 165 and 435, to get
435 = 165 x 2 + 105
Step 3: We consider the new divisor 165 and the new remainder 105, and apply the division lemma to get
165 = 105 x 1 + 60
We consider the new divisor 105 and the new remainder 60,and apply the division lemma to get
105 = 60 x 1 + 45
We consider the new divisor 60 and the new remainder 45,and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 435 and 600 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(105,60) = HCF(165,105) = HCF(435,165) = HCF(600,435) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 261 > 15, we apply the division lemma to 261 and 15, to get
261 = 15 x 17 + 6
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 6 and 15, to get
15 = 6 x 2 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 261 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(261,15) .
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Frequently Asked Questions on HCF of 435, 600, 261 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 435, 600, 261?
Answer: HCF of 435, 600, 261 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 435, 600, 261 using Euclid's Algorithm?
Answer: For arbitrary numbers 435, 600, 261 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.