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, 698, 415 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 240, 698, 415 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 240, 698, 415 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, 698, 415 is 1.
HCF(240, 698, 415) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 240, 698, 415 is 1.
Step 1: Since 698 > 240, we apply the division lemma to 698 and 240, to get
698 = 240 x 2 + 218
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 218 and 240, to get
240 = 218 x 1 + 22
Step 3: We consider the new divisor 218 and the new remainder 22, and apply the division lemma to get
218 = 22 x 9 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 240 and 698 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(218,22) = HCF(240,218) = HCF(698,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 415 > 2, we apply the division lemma to 415 and 2, to get
415 = 2 x 207 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 415 is 1
Notice that 1 = HCF(2,1) = HCF(415,2) .
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 240, 698, 415?
Answer: HCF of 240, 698, 415 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 240, 698, 415 using Euclid's Algorithm?
Answer: For arbitrary numbers 240, 698, 415 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.