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 9015, 1975 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 9015, 1975 is 5 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 9015, 1975 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 9015, 1975 is 5.
HCF(9015, 1975) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9015, 1975 is 5.
Step 1: Since 9015 > 1975, we apply the division lemma to 9015 and 1975, to get
9015 = 1975 x 4 + 1115
Step 2: Since the reminder 1975 ≠ 0, we apply division lemma to 1115 and 1975, to get
1975 = 1115 x 1 + 860
Step 3: We consider the new divisor 1115 and the new remainder 860, and apply the division lemma to get
1115 = 860 x 1 + 255
We consider the new divisor 860 and the new remainder 255,and apply the division lemma to get
860 = 255 x 3 + 95
We consider the new divisor 255 and the new remainder 95,and apply the division lemma to get
255 = 95 x 2 + 65
We consider the new divisor 95 and the new remainder 65,and apply the division lemma to get
95 = 65 x 1 + 30
We consider the new divisor 65 and the new remainder 30,and apply the division lemma to get
65 = 30 x 2 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 9015 and 1975 is 5
Notice that 5 = HCF(30,5) = HCF(65,30) = HCF(95,65) = HCF(255,95) = HCF(860,255) = HCF(1115,860) = HCF(1975,1115) = HCF(9015,1975) .
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 9015, 1975?
Answer: HCF of 9015, 1975 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9015, 1975 using Euclid's Algorithm?
Answer: For arbitrary numbers 9015, 1975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.