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 120, 480, 168 i.e. 24 the largest integer that leaves a remainder zero for all numbers.
HCF of 120, 480, 168 is 24 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 120, 480, 168 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 120, 480, 168 is 24.
HCF(120, 480, 168) = 24
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 120, 480, 168 is 24.
Step 1: Since 480 > 120, we apply the division lemma to 480 and 120, to get
480 = 120 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 120, the HCF of 120 and 480 is 120
Notice that 120 = HCF(480,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 168 > 120, we apply the division lemma to 168 and 120, to get
168 = 120 x 1 + 48
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 48 and 120, to get
120 = 48 x 2 + 24
Step 3: We consider the new divisor 48 and the new remainder 24, and apply the division lemma to get
48 = 24 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 120 and 168 is 24
Notice that 24 = HCF(48,24) = HCF(120,48) = HCF(168,120) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 120, 480, 168?
Answer: HCF of 120, 480, 168 is 24 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 120, 480, 168 using Euclid's Algorithm?
Answer: For arbitrary numbers 120, 480, 168 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.