Highest Common Factor of 8505, 9945 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 8505, 9945 i.e. 45 the largest integer that leaves a remainder zero for all numbers.
HCF of 8505, 9945 is 45 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 8505, 9945 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 8505, 9945 is 45.
HCF(8505, 9945) = 45
HCF of 8505, 9945 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8505, 9945 is 45.
Highest Common Factor of 8505,9945 is 45
Step 1: Since 9945 > 8505, we apply the division lemma to 9945 and 8505, to get
9945 = 8505 x 1 + 1440
Step 2: Since the reminder 8505 ≠ 0, we apply division lemma to 1440 and 8505, to get
8505 = 1440 x 5 + 1305
Step 3: We consider the new divisor 1440 and the new remainder 1305, and apply the division lemma to get
1440 = 1305 x 1 + 135
We consider the new divisor 1305 and the new remainder 135,and apply the division lemma to get
1305 = 135 x 9 + 90
We consider the new divisor 135 and the new remainder 90,and apply the division lemma to get
135 = 90 x 1 + 45
We consider the new divisor 90 and the new remainder 45,and apply the division lemma to get
90 = 45 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 8505 and 9945 is 45
Notice that 45 = HCF(90,45) = HCF(135,90) = HCF(1305,135) = HCF(1440,1305) = HCF(8505,1440) = HCF(9945,8505) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8505, 9945 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 8505, 9945?
Answer: HCF of 8505, 9945 is 45 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8505, 9945 using Euclid's Algorithm?
Answer: For arbitrary numbers 8505, 9945 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.