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 417, 240, 996 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 417, 240, 996 is 3 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 417, 240, 996 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 417, 240, 996 is 3.
HCF(417, 240, 996) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 417, 240, 996 is 3.
Step 1: Since 417 > 240, we apply the division lemma to 417 and 240, to get
417 = 240 x 1 + 177
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 177 and 240, to get
240 = 177 x 1 + 63
Step 3: We consider the new divisor 177 and the new remainder 63, and apply the division lemma to get
177 = 63 x 2 + 51
We consider the new divisor 63 and the new remainder 51,and apply the division lemma to get
63 = 51 x 1 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 417 and 240 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(63,51) = HCF(177,63) = HCF(240,177) = HCF(417,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 996 > 3, we apply the division lemma to 996 and 3, to get
996 = 3 x 332 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 996 is 3
Notice that 3 = HCF(996,3) .
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 417, 240, 996?
Answer: HCF of 417, 240, 996 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 417, 240, 996 using Euclid's Algorithm?
Answer: For arbitrary numbers 417, 240, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.