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 240, 378, 198 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 240, 378, 198 is 6 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 240, 378, 198 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 240, 378, 198 is 6.
HCF(240, 378, 198) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 240, 378, 198 is 6.
Step 1: Since 378 > 240, we apply the division lemma to 378 and 240, to get
378 = 240 x 1 + 138
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 138 and 240, to get
240 = 138 x 1 + 102
Step 3: We consider the new divisor 138 and the new remainder 102, and apply the division lemma to get
138 = 102 x 1 + 36
We consider the new divisor 102 and the new remainder 36,and apply the division lemma to get
102 = 36 x 2 + 30
We consider the new divisor 36 and the new remainder 30,and apply the division lemma to get
36 = 30 x 1 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 240 and 378 is 6
Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(102,36) = HCF(138,102) = HCF(240,138) = HCF(378,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 198 > 6, we apply the division lemma to 198 and 6, to get
198 = 6 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 198 is 6
Notice that 6 = HCF(198,6) .
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 240, 378, 198?
Answer: HCF of 240, 378, 198 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 240, 378, 198 using Euclid's Algorithm?
Answer: For arbitrary numbers 240, 378, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.