Highest Common Factor of 60, 135, 105 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 60, 135, 105 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 60, 135, 105 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 60, 135, 105 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 60, 135, 105 is 15.
HCF(60, 135, 105) = 15
HCF of 60, 135, 105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 60, 135, 105 is 15.
Highest Common Factor of 60,135,105 is 15
Step 1: Since 135 > 60, we apply the division lemma to 135 and 60, to get
135 = 60 x 2 + 15
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 15 and 60, to get
60 = 15 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 60 and 135 is 15
Notice that 15 = HCF(60,15) = HCF(135,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 15, we apply the division lemma to 105 and 15, 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 15 and 105 is 15
Notice that 15 = HCF(105,15) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 60, 135, 105 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 60, 135, 105?
Answer: HCF of 60, 135, 105 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 60, 135, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 60, 135, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.