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 662, 9804, 5708 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 662, 9804, 5708 is 2 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 662, 9804, 5708 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 662, 9804, 5708 is 2.
HCF(662, 9804, 5708) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 662, 9804, 5708 is 2.
Step 1: Since 9804 > 662, we apply the division lemma to 9804 and 662, to get
9804 = 662 x 14 + 536
Step 2: Since the reminder 662 ≠ 0, we apply division lemma to 536 and 662, to get
662 = 536 x 1 + 126
Step 3: We consider the new divisor 536 and the new remainder 126, and apply the division lemma to get
536 = 126 x 4 + 32
We consider the new divisor 126 and the new remainder 32,and apply the division lemma to get
126 = 32 x 3 + 30
We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get
32 = 30 x 1 + 2
We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 662 and 9804 is 2
Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(126,32) = HCF(536,126) = HCF(662,536) = HCF(9804,662) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5708 > 2, we apply the division lemma to 5708 and 2, to get
5708 = 2 x 2854 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 5708 is 2
Notice that 2 = HCF(5708,2) .
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 662, 9804, 5708?
Answer: HCF of 662, 9804, 5708 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 662, 9804, 5708 using Euclid's Algorithm?
Answer: For arbitrary numbers 662, 9804, 5708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.