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 825, 970 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 970 is 5 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 825, 970 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 825, 970 is 5.
HCF(825, 970) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 825, 970 is 5.
Step 1: Since 970 > 825, we apply the division lemma to 970 and 825, to get
970 = 825 x 1 + 145
Step 2: Since the reminder 825 ≠ 0, we apply division lemma to 145 and 825, to get
825 = 145 x 5 + 100
Step 3: We consider the new divisor 145 and the new remainder 100, and apply the division lemma to get
145 = 100 x 1 + 45
We consider the new divisor 100 and the new remainder 45,and apply the division lemma to get
100 = 45 x 2 + 10
We consider the new divisor 45 and the new remainder 10,and apply the division lemma to get
45 = 10 x 4 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 825 and 970 is 5
Notice that 5 = HCF(10,5) = HCF(45,10) = HCF(100,45) = HCF(145,100) = HCF(825,145) = HCF(970,825) .
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 825, 970?
Answer: HCF of 825, 970 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 970 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.