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 478, 1020, 9932 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 478, 1020, 9932 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 478, 1020, 9932 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 478, 1020, 9932 is 2.
HCF(478, 1020, 9932) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 478, 1020, 9932 is 2.
Step 1: Since 1020 > 478, we apply the division lemma to 1020 and 478, to get
1020 = 478 x 2 + 64
Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 64 and 478, to get
478 = 64 x 7 + 30
Step 3: We consider the new divisor 64 and the new remainder 30, and apply the division lemma to get
64 = 30 x 2 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 478 and 1020 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(64,30) = HCF(478,64) = HCF(1020,478) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9932 > 2, we apply the division lemma to 9932 and 2, to get
9932 = 2 x 4966 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9932 is 2
Notice that 2 = HCF(9932,2) .
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 478, 1020, 9932?
Answer: HCF of 478, 1020, 9932 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 478, 1020, 9932 using Euclid's Algorithm?
Answer: For arbitrary numbers 478, 1020, 9932 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.