Highest Common Factor of 1089, 6405 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 1089, 6405 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1089, 6405 is 3 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 1089, 6405 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 1089, 6405 is 3.
HCF(1089, 6405) = 3
HCF of 1089, 6405 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1089, 6405 is 3.
Highest Common Factor of 1089,6405 is 3
Step 1: Since 6405 > 1089, we apply the division lemma to 6405 and 1089, to get
6405 = 1089 x 5 + 960
Step 2: Since the reminder 1089 ≠ 0, we apply division lemma to 960 and 1089, to get
1089 = 960 x 1 + 129
Step 3: We consider the new divisor 960 and the new remainder 129, and apply the division lemma to get
960 = 129 x 7 + 57
We consider the new divisor 129 and the new remainder 57,and apply the division lemma to get
129 = 57 x 2 + 15
We consider the new divisor 57 and the new remainder 15,and apply the division lemma to get
57 = 15 x 3 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1089 and 6405 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(57,15) = HCF(129,57) = HCF(960,129) = HCF(1089,960) = HCF(6405,1089) .
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Frequently Asked Questions on HCF of 1089, 6405 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 1089, 6405?
Answer: HCF of 1089, 6405 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1089, 6405 using Euclid's Algorithm?
Answer: For arbitrary numbers 1089, 6405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.