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, 558, 615 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 465, 558, 615 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, 558, 615 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, 558, 615 is 3.
HCF(465, 558, 615) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 465, 558, 615 is 3.
Step 1: Since 558 > 465, we apply the division lemma to 558 and 465, to get
558 = 465 x 1 + 93
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 93 and 465, to get
465 = 93 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 93, the HCF of 465 and 558 is 93
Notice that 93 = HCF(465,93) = HCF(558,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 615 > 93, we apply the division lemma to 615 and 93, to get
615 = 93 x 6 + 57
Step 2: Since the reminder 93 ≠ 0, we apply division lemma to 57 and 93, to get
93 = 57 x 1 + 36
Step 3: We consider the new divisor 57 and the new remainder 36, and apply the division lemma to get
57 = 36 x 1 + 21
We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 93 and 615 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(57,36) = HCF(93,57) = HCF(615,93) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 558, 615?
Answer: HCF of 465, 558, 615 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 465, 558, 615 using Euclid's Algorithm?
Answer: For arbitrary numbers 465, 558, 615 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.