Highest Common Factor of 18, 50, 60, 119 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 18, 50, 60, 119 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 18, 50, 60, 119 is 1 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 18, 50, 60, 119 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 18, 50, 60, 119 is 1.
HCF(18, 50, 60, 119) = 1
HCF of 18, 50, 60, 119 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 18, 50, 60, 119 is 1.
Highest Common Factor of 18,50,60,119 is 1
Step 1: Since 50 > 18, we apply the division lemma to 50 and 18, to get
50 = 18 x 2 + 14
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 14 and 18, to get
18 = 14 x 1 + 4
Step 3: We consider the new divisor 14 and the new remainder 4, and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 50 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(50,18) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 2, we apply the division lemma to 60 and 2, to get
60 = 2 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 60 is 2
Notice that 2 = HCF(60,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 119 > 2, we apply the division lemma to 119 and 2, to get
119 = 2 x 59 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 119 is 1
Notice that 1 = HCF(2,1) = HCF(119,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 18, 50, 60, 119 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 18, 50, 60, 119?
Answer: HCF of 18, 50, 60, 119 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 18, 50, 60, 119 using Euclid's Algorithm?
Answer: For arbitrary numbers 18, 50, 60, 119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.