Highest Common Factor of 315, 966, 345 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 315, 966, 345 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 315, 966, 345 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 315, 966, 345 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 315, 966, 345 is 3.
HCF(315, 966, 345) = 3
HCF of 315, 966, 345 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 315, 966, 345 is 3.
Highest Common Factor of 315,966,345 is 3
Step 1: Since 966 > 315, we apply the division lemma to 966 and 315, to get
966 = 315 x 3 + 21
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 21 and 315, to get
315 = 21 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 315 and 966 is 21
Notice that 21 = HCF(315,21) = HCF(966,315) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 345 > 21, we apply the division lemma to 345 and 21, to get
345 = 21 x 16 + 9
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 9 and 21, to get
21 = 9 x 2 + 3
Step 3: We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 345 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(345,21) .
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Frequently Asked Questions on HCF of 315, 966, 345 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 315, 966, 345?
Answer: HCF of 315, 966, 345 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 315, 966, 345 using Euclid's Algorithm?
Answer: For arbitrary numbers 315, 966, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.