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 508, 909, 39 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 508, 909, 39 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 508, 909, 39 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 508, 909, 39 is 1.
HCF(508, 909, 39) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 508, 909, 39 is 1.
Step 1: Since 909 > 508, we apply the division lemma to 909 and 508, to get
909 = 508 x 1 + 401
Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 401 and 508, to get
508 = 401 x 1 + 107
Step 3: We consider the new divisor 401 and the new remainder 107, and apply the division lemma to get
401 = 107 x 3 + 80
We consider the new divisor 107 and the new remainder 80,and apply the division lemma to get
107 = 80 x 1 + 27
We consider the new divisor 80 and the new remainder 27,and apply the division lemma to get
80 = 27 x 2 + 26
We consider the new divisor 27 and the new remainder 26,and apply the division lemma to get
27 = 26 x 1 + 1
We consider the new divisor 26 and the new remainder 1,and apply the division lemma to get
26 = 1 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 508 and 909 is 1
Notice that 1 = HCF(26,1) = HCF(27,26) = HCF(80,27) = HCF(107,80) = HCF(401,107) = HCF(508,401) = HCF(909,508) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 39 > 1, we apply the division lemma to 39 and 1, to get
39 = 1 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 39 is 1
Notice that 1 = HCF(39,1) .
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 508, 909, 39?
Answer: HCF of 508, 909, 39 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 508, 909, 39 using Euclid's Algorithm?
Answer: For arbitrary numbers 508, 909, 39 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.