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 711, 408, 636 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 711, 408, 636 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 711, 408, 636 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 711, 408, 636 is 3.
HCF(711, 408, 636) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 711, 408, 636 is 3.
Step 1: Since 711 > 408, we apply the division lemma to 711 and 408, to get
711 = 408 x 1 + 303
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 303 and 408, to get
408 = 303 x 1 + 105
Step 3: We consider the new divisor 303 and the new remainder 105, and apply the division lemma to get
303 = 105 x 2 + 93
We consider the new divisor 105 and the new remainder 93,and apply the division lemma to get
105 = 93 x 1 + 12
We consider the new divisor 93 and the new remainder 12,and apply the division lemma to get
93 = 12 x 7 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 711 and 408 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(93,12) = HCF(105,93) = HCF(303,105) = HCF(408,303) = HCF(711,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 636 > 3, we apply the division lemma to 636 and 3, to get
636 = 3 x 212 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 636 is 3
Notice that 3 = HCF(636,3) .
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 711, 408, 636?
Answer: HCF of 711, 408, 636 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 711, 408, 636 using Euclid's Algorithm?
Answer: For arbitrary numbers 711, 408, 636 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.