Highest Common Factor of 465, 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 465, 345 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 465, 345 is 15 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, 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 465, 345 is 15.
HCF(465, 345) = 15
HCF of 465, 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 465, 345 is 15.
Highest Common Factor of 465,345 is 15
Step 1: Since 465 > 345, we apply the division lemma to 465 and 345, to get
465 = 345 x 1 + 120
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 120 and 345, to get
345 = 120 x 2 + 105
Step 3: We consider the new divisor 120 and the new remainder 105, and apply the division lemma to get
120 = 105 x 1 + 15
We consider the new divisor 105 and the new remainder 15, and apply the division lemma to get
105 = 15 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 465 and 345 is 15
Notice that 15 = HCF(105,15) = HCF(120,105) = HCF(345,120) = HCF(465,345) .
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Frequently Asked Questions on HCF of 465, 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 465, 345?
Answer: HCF of 465, 345 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 465, 345 using Euclid's Algorithm?
Answer: For arbitrary numbers 465, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.