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 9987, 1058 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9987, 1058 is 1 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 9987, 1058 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 9987, 1058 is 1.
HCF(9987, 1058) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9987, 1058 is 1.
Step 1: Since 9987 > 1058, we apply the division lemma to 9987 and 1058, to get
9987 = 1058 x 9 + 465
Step 2: Since the reminder 1058 ≠ 0, we apply division lemma to 465 and 1058, to get
1058 = 465 x 2 + 128
Step 3: We consider the new divisor 465 and the new remainder 128, and apply the division lemma to get
465 = 128 x 3 + 81
We consider the new divisor 128 and the new remainder 81,and apply the division lemma to get
128 = 81 x 1 + 47
We consider the new divisor 81 and the new remainder 47,and apply the division lemma to get
81 = 47 x 1 + 34
We consider the new divisor 47 and the new remainder 34,and apply the division lemma to get
47 = 34 x 1 + 13
We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get
34 = 13 x 2 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9987 and 1058 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(47,34) = HCF(81,47) = HCF(128,81) = HCF(465,128) = HCF(1058,465) = HCF(9987,1058) .
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 9987, 1058?
Answer: HCF of 9987, 1058 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9987, 1058 using Euclid's Algorithm?
Answer: For arbitrary numbers 9987, 1058 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.