Highest Common Factor of 465, 915, 342 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 465, 915, 342 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 465, 915, 342 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 465, 915, 342 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 465, 915, 342 is 3.
HCF(465, 915, 342) = 3
HCF of 465, 915, 342 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 465, 915, 342 is 3.
Highest Common Factor of 465,915,342 is 3
Step 1: Since 915 > 465, we apply the division lemma to 915 and 465, to get
915 = 465 x 1 + 450
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 450 and 465, to get
465 = 450 x 1 + 15
Step 3: We consider the new divisor 450 and the new remainder 15, and apply the division lemma to get
450 = 15 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 465 and 915 is 15
Notice that 15 = HCF(450,15) = HCF(465,450) = HCF(915,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 342 > 15, we apply the division lemma to 342 and 15, to get
342 = 15 x 22 + 12
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 12 and 15, to get
15 = 12 x 1 + 3
Step 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 15 and 342 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(342,15) .
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Frequently Asked Questions on HCF of 465, 915, 342 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 465, 915, 342?
Answer: HCF of 465, 915, 342 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 465, 915, 342 using Euclid's Algorithm?
Answer: For arbitrary numbers 465, 915, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.