Highest Common Factor of 410, 610, 988 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 410, 610, 988 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 610, 988 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 410, 610, 988 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 410, 610, 988 is 2.
HCF(410, 610, 988) = 2
HCF of 410, 610, 988 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 410, 610, 988 is 2.
Highest Common Factor of 410,610,988 is 2
Step 1: Since 610 > 410, we apply the division lemma to 610 and 410, to get
610 = 410 x 1 + 200
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 200 and 410, to get
410 = 200 x 2 + 10
Step 3: We consider the new divisor 200 and the new remainder 10, and apply the division lemma to get
200 = 10 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 410 and 610 is 10
Notice that 10 = HCF(200,10) = HCF(410,200) = HCF(610,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 988 > 10, we apply the division lemma to 988 and 10, to get
988 = 10 x 98 + 8
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 8 and 10, to get
10 = 8 x 1 + 2
Step 3: We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 988 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(988,10) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 410, 610, 988 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 410, 610, 988?
Answer: HCF of 410, 610, 988 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 610, 988 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 610, 988 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.