Highest Common Factor of 945, 7683 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 945, 7683 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 945, 7683 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 945, 7683 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 945, 7683 is 3.
HCF(945, 7683) = 3
HCF of 945, 7683 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 945, 7683 is 3.
Highest Common Factor of 945,7683 is 3
Step 1: Since 7683 > 945, we apply the division lemma to 7683 and 945, to get
7683 = 945 x 8 + 123
Step 2: Since the reminder 945 ≠ 0, we apply division lemma to 123 and 945, to get
945 = 123 x 7 + 84
Step 3: We consider the new divisor 123 and the new remainder 84, and apply the division lemma to get
123 = 84 x 1 + 39
We consider the new divisor 84 and the new remainder 39,and apply the division lemma to get
84 = 39 x 2 + 6
We consider the new divisor 39 and the new remainder 6,and apply the division lemma to get
39 = 6 x 6 + 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 945 and 7683 is 3
Notice that 3 = HCF(6,3) = HCF(39,6) = HCF(84,39) = HCF(123,84) = HCF(945,123) = HCF(7683,945) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 945, 7683 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 945, 7683?
Answer: HCF of 945, 7683 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 945, 7683 using Euclid's Algorithm?
Answer: For arbitrary numbers 945, 7683 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.