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 984, 651, 585, 36 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 984, 651, 585, 36 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 984, 651, 585, 36 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 984, 651, 585, 36 is 3.
HCF(984, 651, 585, 36) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 984, 651, 585, 36 is 3.
Step 1: Since 984 > 651, we apply the division lemma to 984 and 651, to get
984 = 651 x 1 + 333
Step 2: Since the reminder 651 ≠ 0, we apply division lemma to 333 and 651, to get
651 = 333 x 1 + 318
Step 3: We consider the new divisor 333 and the new remainder 318, and apply the division lemma to get
333 = 318 x 1 + 15
We consider the new divisor 318 and the new remainder 15,and apply the division lemma to get
318 = 15 x 21 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 984 and 651 is 3
Notice that 3 = HCF(15,3) = HCF(318,15) = HCF(333,318) = HCF(651,333) = HCF(984,651) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 585 > 3, we apply the division lemma to 585 and 3, to get
585 = 3 x 195 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 585 is 3
Notice that 3 = HCF(585,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 36 > 3, we apply the division lemma to 36 and 3, to get
36 = 3 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 36 is 3
Notice that 3 = HCF(36,3) .
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 984, 651, 585, 36?
Answer: HCF of 984, 651, 585, 36 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 984, 651, 585, 36 using Euclid's Algorithm?
Answer: For arbitrary numbers 984, 651, 585, 36 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.