Highest Common Factor of 996, 636, 366 using Euclid's algorithm
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 996, 636, 366 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 636, 366 is 6 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 996, 636, 366 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 996, 636, 366 is 6.
HCF(996, 636, 366) = 6
HCF of 996, 636, 366 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 996, 636, 366 is 6.
Highest Common Factor of 996,636,366 is 6
Step 1: Since 996 > 636, we apply the division lemma to 996 and 636, to get
996 = 636 x 1 + 360
Step 2: Since the reminder 636 ≠ 0, we apply division lemma to 360 and 636, to get
636 = 360 x 1 + 276
Step 3: We consider the new divisor 360 and the new remainder 276, and apply the division lemma to get
360 = 276 x 1 + 84
We consider the new divisor 276 and the new remainder 84,and apply the division lemma to get
276 = 84 x 3 + 24
We consider the new divisor 84 and the new remainder 24,and apply the division lemma to get
84 = 24 x 3 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 996 and 636 is 12
Notice that 12 = HCF(24,12) = HCF(84,24) = HCF(276,84) = HCF(360,276) = HCF(636,360) = HCF(996,636) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 366 > 12, we apply the division lemma to 366 and 12, to get
366 = 12 x 30 + 6
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 12 and 366 is 6
Notice that 6 = HCF(12,6) = HCF(366,12) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 996, 636, 366 using Euclid's Algorithm
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 996, 636, 366?
Answer: HCF of 996, 636, 366 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 636, 366 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 636, 366 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.