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 960, 9910, 3878 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 960, 9910, 3878 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 960, 9910, 3878 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 960, 9910, 3878 is 2.
HCF(960, 9910, 3878) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 960, 9910, 3878 is 2.
Step 1: Since 9910 > 960, we apply the division lemma to 9910 and 960, to get
9910 = 960 x 10 + 310
Step 2: Since the reminder 960 ≠ 0, we apply division lemma to 310 and 960, to get
960 = 310 x 3 + 30
Step 3: We consider the new divisor 310 and the new remainder 30, and apply the division lemma to get
310 = 30 x 10 + 10
We consider the new divisor 30 and the new remainder 10, and apply the division lemma to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 960 and 9910 is 10
Notice that 10 = HCF(30,10) = HCF(310,30) = HCF(960,310) = HCF(9910,960) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3878 > 10, we apply the division lemma to 3878 and 10, to get
3878 = 10 x 387 + 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 3878 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(3878,10) .
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 960, 9910, 3878?
Answer: HCF of 960, 9910, 3878 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 960, 9910, 3878 using Euclid's Algorithm?
Answer: For arbitrary numbers 960, 9910, 3878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.