Highest Common Factor of 170, 120, 33 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 170, 120, 33 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 170, 120, 33 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 170, 120, 33 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 170, 120, 33 is 1.
HCF(170, 120, 33) = 1
HCF of 170, 120, 33 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 170, 120, 33 is 1.
Highest Common Factor of 170,120,33 is 1
Step 1: Since 170 > 120, we apply the division lemma to 170 and 120, to get
170 = 120 x 1 + 50
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 50 and 120, to get
120 = 50 x 2 + 20
Step 3: We consider the new divisor 50 and the new remainder 20, and apply the division lemma to get
50 = 20 x 2 + 10
We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 170 and 120 is 10
Notice that 10 = HCF(20,10) = HCF(50,20) = HCF(120,50) = HCF(170,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 33 > 10, we apply the division lemma to 33 and 10, to get
33 = 10 x 3 + 3
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 3 and 10, to get
10 = 3 x 3 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 33 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(33,10) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 170, 120, 33 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 170, 120, 33?
Answer: HCF of 170, 120, 33 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 170, 120, 33 using Euclid's Algorithm?
Answer: For arbitrary numbers 170, 120, 33 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.