Highest Common Factor of 915, 714, 162 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 915, 714, 162 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 915, 714, 162 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 915, 714, 162 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 915, 714, 162 is 3.
HCF(915, 714, 162) = 3
HCF of 915, 714, 162 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 915, 714, 162 is 3.
Highest Common Factor of 915,714,162 is 3
Step 1: Since 915 > 714, we apply the division lemma to 915 and 714, to get
915 = 714 x 1 + 201
Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 201 and 714, to get
714 = 201 x 3 + 111
Step 3: We consider the new divisor 201 and the new remainder 111, and apply the division lemma to get
201 = 111 x 1 + 90
We consider the new divisor 111 and the new remainder 90,and apply the division lemma to get
111 = 90 x 1 + 21
We consider the new divisor 90 and the new remainder 21,and apply the division lemma to get
90 = 21 x 4 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 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 915 and 714 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(90,21) = HCF(111,90) = HCF(201,111) = HCF(714,201) = HCF(915,714) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 162 > 3, we apply the division lemma to 162 and 3, to get
162 = 3 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 162 is 3
Notice that 3 = HCF(162,3) .
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Frequently Asked Questions on HCF of 915, 714, 162 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 915, 714, 162?
Answer: HCF of 915, 714, 162 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 915, 714, 162 using Euclid's Algorithm?
Answer: For arbitrary numbers 915, 714, 162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.