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 762, 40971 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 762, 40971 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 762, 40971 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 762, 40971 is 3.
HCF(762, 40971) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 762, 40971 is 3.
Step 1: Since 40971 > 762, we apply the division lemma to 40971 and 762, to get
40971 = 762 x 53 + 585
Step 2: Since the reminder 762 ≠ 0, we apply division lemma to 585 and 762, to get
762 = 585 x 1 + 177
Step 3: We consider the new divisor 585 and the new remainder 177, and apply the division lemma to get
585 = 177 x 3 + 54
We consider the new divisor 177 and the new remainder 54,and apply the division lemma to get
177 = 54 x 3 + 15
We consider the new divisor 54 and the new remainder 15,and apply the division lemma to get
54 = 15 x 3 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 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 762 and 40971 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(177,54) = HCF(585,177) = HCF(762,585) = HCF(40971,762) .
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 762, 40971?
Answer: HCF of 762, 40971 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 762, 40971 using Euclid's Algorithm?
Answer: For arbitrary numbers 762, 40971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.