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 7500, 7689 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 7500, 7689 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 7500, 7689 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 7500, 7689 is 3.
HCF(7500, 7689) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7500, 7689 is 3.
Step 1: Since 7689 > 7500, we apply the division lemma to 7689 and 7500, to get
7689 = 7500 x 1 + 189
Step 2: Since the reminder 7500 ≠ 0, we apply division lemma to 189 and 7500, to get
7500 = 189 x 39 + 129
Step 3: We consider the new divisor 189 and the new remainder 129, and apply the division lemma to get
189 = 129 x 1 + 60
We consider the new divisor 129 and the new remainder 60,and apply the division lemma to get
129 = 60 x 2 + 9
We consider the new divisor 60 and the new remainder 9,and apply the division lemma to get
60 = 9 x 6 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 7500 and 7689 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) = HCF(129,60) = HCF(189,129) = HCF(7500,189) = HCF(7689,7500) .
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 7500, 7689?
Answer: HCF of 7500, 7689 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7500, 7689 using Euclid's Algorithm?
Answer: For arbitrary numbers 7500, 7689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.