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 415, 709, 10 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 415, 709, 10 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 415, 709, 10 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 415, 709, 10 is 1.
HCF(415, 709, 10) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 415, 709, 10 is 1.
Step 1: Since 709 > 415, we apply the division lemma to 709 and 415, to get
709 = 415 x 1 + 294
Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 294 and 415, to get
415 = 294 x 1 + 121
Step 3: We consider the new divisor 294 and the new remainder 121, and apply the division lemma to get
294 = 121 x 2 + 52
We consider the new divisor 121 and the new remainder 52,and apply the division lemma to get
121 = 52 x 2 + 17
We consider the new divisor 52 and the new remainder 17,and apply the division lemma to get
52 = 17 x 3 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 415 and 709 is 1
Notice that 1 = HCF(17,1) = HCF(52,17) = HCF(121,52) = HCF(294,121) = HCF(415,294) = HCF(709,415) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 10 > 1, we apply the division lemma to 10 and 1, to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 10 is 1
Notice that 1 = HCF(10,1) .
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 415, 709, 10?
Answer: HCF of 415, 709, 10 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 415, 709, 10 using Euclid's Algorithm?
Answer: For arbitrary numbers 415, 709, 10 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.