Highest Common Factor of 372, 609, 405 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 372, 609, 405 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 609, 405 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 372, 609, 405 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 372, 609, 405 is 3.
HCF(372, 609, 405) = 3
HCF of 372, 609, 405 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 372, 609, 405 is 3.
Highest Common Factor of 372,609,405 is 3
Step 1: Since 609 > 372, we apply the division lemma to 609 and 372, to get
609 = 372 x 1 + 237
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 237 and 372, to get
372 = 237 x 1 + 135
Step 3: We consider the new divisor 237 and the new remainder 135, and apply the division lemma to get
237 = 135 x 1 + 102
We consider the new divisor 135 and the new remainder 102,and apply the division lemma to get
135 = 102 x 1 + 33
We consider the new divisor 102 and the new remainder 33,and apply the division lemma to get
102 = 33 x 3 + 3
We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 372 and 609 is 3
Notice that 3 = HCF(33,3) = HCF(102,33) = HCF(135,102) = HCF(237,135) = HCF(372,237) = HCF(609,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 405 > 3, we apply the division lemma to 405 and 3, to get
405 = 3 x 135 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 405 is 3
Notice that 3 = HCF(405,3) .
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Frequently Asked Questions on HCF of 372, 609, 405 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 372, 609, 405?
Answer: HCF of 372, 609, 405 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 609, 405 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 609, 405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.