Highest Common Factor of 789, 2265, 7735 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 789, 2265, 7735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 789, 2265, 7735 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 789, 2265, 7735 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 789, 2265, 7735 is 1.
HCF(789, 2265, 7735) = 1
HCF of 789, 2265, 7735 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 789, 2265, 7735 is 1.
Highest Common Factor of 789,2265,7735 is 1
Step 1: Since 2265 > 789, we apply the division lemma to 2265 and 789, to get
2265 = 789 x 2 + 687
Step 2: Since the reminder 789 ≠ 0, we apply division lemma to 687 and 789, to get
789 = 687 x 1 + 102
Step 3: We consider the new divisor 687 and the new remainder 102, and apply the division lemma to get
687 = 102 x 6 + 75
We consider the new divisor 102 and the new remainder 75,and apply the division lemma to get
102 = 75 x 1 + 27
We consider the new divisor 75 and the new remainder 27,and apply the division lemma to get
75 = 27 x 2 + 21
We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get
27 = 21 x 1 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 789 and 2265 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(75,27) = HCF(102,75) = HCF(687,102) = HCF(789,687) = HCF(2265,789) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7735 > 3, we apply the division lemma to 7735 and 3, to get
7735 = 3 x 2578 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 7735 is 1
Notice that 1 = HCF(3,1) = HCF(7735,3) .
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Frequently Asked Questions on HCF of 789, 2265, 7735 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 789, 2265, 7735?
Answer: HCF of 789, 2265, 7735 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 789, 2265, 7735 using Euclid's Algorithm?
Answer: For arbitrary numbers 789, 2265, 7735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.