Highest Common Factor of 108, 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 108, 915, 342 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 108, 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 108, 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 108, 915, 342 is 3.
HCF(108, 915, 342) = 3
HCF of 108, 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 108, 915, 342 is 3.
Highest Common Factor of 108,915,342 is 3
Step 1: Since 915 > 108, we apply the division lemma to 915 and 108, to get
915 = 108 x 8 + 51
Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 51 and 108, to get
108 = 51 x 2 + 6
Step 3: We consider the new divisor 51 and the new remainder 6, and apply the division lemma to get
51 = 6 x 8 + 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 108 and 915 is 3
Notice that 3 = HCF(6,3) = HCF(51,6) = HCF(108,51) = HCF(915,108) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 342 > 3, we apply the division lemma to 342 and 3, to get
342 = 3 x 114 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 342 is 3
Notice that 3 = HCF(342,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 108, 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 108, 915, 342?
Answer: HCF of 108, 915, 342 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 108, 915, 342 using Euclid's Algorithm?
Answer: For arbitrary numbers 108, 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.