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 238, 7192, 2004 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 238, 7192, 2004 is 2 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 238, 7192, 2004 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 238, 7192, 2004 is 2.
HCF(238, 7192, 2004) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 238, 7192, 2004 is 2.
Step 1: Since 7192 > 238, we apply the division lemma to 7192 and 238, to get
7192 = 238 x 30 + 52
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 52 and 238, to get
238 = 52 x 4 + 30
Step 3: We consider the new divisor 52 and the new remainder 30, and apply the division lemma to get
52 = 30 x 1 + 22
We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get
30 = 22 x 1 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 238 and 7192 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(52,30) = HCF(238,52) = HCF(7192,238) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2004 > 2, we apply the division lemma to 2004 and 2, to get
2004 = 2 x 1002 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 2004 is 2
Notice that 2 = HCF(2004,2) .
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 238, 7192, 2004?
Answer: HCF of 238, 7192, 2004 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 238, 7192, 2004 using Euclid's Algorithm?
Answer: For arbitrary numbers 238, 7192, 2004 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.