Highest Common Factor of 2975, 6982 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 2975, 6982 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2975, 6982 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 2975, 6982 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 2975, 6982 is 1.
HCF(2975, 6982) = 1
HCF of 2975, 6982 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2975, 6982 is 1.
Highest Common Factor of 2975,6982 is 1
Step 1: Since 6982 > 2975, we apply the division lemma to 6982 and 2975, to get
6982 = 2975 x 2 + 1032
Step 2: Since the reminder 2975 ≠ 0, we apply division lemma to 1032 and 2975, to get
2975 = 1032 x 2 + 911
Step 3: We consider the new divisor 1032 and the new remainder 911, and apply the division lemma to get
1032 = 911 x 1 + 121
We consider the new divisor 911 and the new remainder 121,and apply the division lemma to get
911 = 121 x 7 + 64
We consider the new divisor 121 and the new remainder 64,and apply the division lemma to get
121 = 64 x 1 + 57
We consider the new divisor 64 and the new remainder 57,and apply the division lemma to get
64 = 57 x 1 + 7
We consider the new divisor 57 and the new remainder 7,and apply the division lemma to get
57 = 7 x 8 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2975 and 6982 is 1
Notice that 1 = HCF(7,1) = HCF(57,7) = HCF(64,57) = HCF(121,64) = HCF(911,121) = HCF(1032,911) = HCF(2975,1032) = HCF(6982,2975) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2975, 6982 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 2975, 6982?
Answer: HCF of 2975, 6982 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2975, 6982 using Euclid's Algorithm?
Answer: For arbitrary numbers 2975, 6982 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.