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 909, 665, 29 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 909, 665, 29 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 909, 665, 29 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 909, 665, 29 is 1.
HCF(909, 665, 29) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 909, 665, 29 is 1.
Step 1: Since 909 > 665, we apply the division lemma to 909 and 665, to get
909 = 665 x 1 + 244
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 244 and 665, to get
665 = 244 x 2 + 177
Step 3: We consider the new divisor 244 and the new remainder 177, and apply the division lemma to get
244 = 177 x 1 + 67
We consider the new divisor 177 and the new remainder 67,and apply the division lemma to get
177 = 67 x 2 + 43
We consider the new divisor 67 and the new remainder 43,and apply the division lemma to get
67 = 43 x 1 + 24
We consider the new divisor 43 and the new remainder 24,and apply the division lemma to get
43 = 24 x 1 + 19
We consider the new divisor 24 and the new remainder 19,and apply the division lemma to get
24 = 19 x 1 + 5
We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get
19 = 5 x 3 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 909 and 665 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(43,24) = HCF(67,43) = HCF(177,67) = HCF(244,177) = HCF(665,244) = HCF(909,665) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 29 > 1, we apply the division lemma to 29 and 1, to get
29 = 1 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 29 is 1
Notice that 1 = HCF(29,1) .
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 909, 665, 29?
Answer: HCF of 909, 665, 29 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 909, 665, 29 using Euclid's Algorithm?
Answer: For arbitrary numbers 909, 665, 29 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.