Highest Common Factor of 974, 825 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 974, 825 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 825 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 974, 825 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 974, 825 is 1.
HCF(974, 825) = 1
HCF of 974, 825 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 825 is 1.
Highest Common Factor of 974,825 is 1
Step 1: Since 974 > 825, we apply the division lemma to 974 and 825, to get
974 = 825 x 1 + 149
Step 2: Since the reminder 825 ≠ 0, we apply division lemma to 149 and 825, to get
825 = 149 x 5 + 80
Step 3: We consider the new divisor 149 and the new remainder 80, and apply the division lemma to get
149 = 80 x 1 + 69
We consider the new divisor 80 and the new remainder 69,and apply the division lemma to get
80 = 69 x 1 + 11
We consider the new divisor 69 and the new remainder 11,and apply the division lemma to get
69 = 11 x 6 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 974 and 825 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(69,11) = HCF(80,69) = HCF(149,80) = HCF(825,149) = HCF(974,825) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 974, 825 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 974, 825?
Answer: HCF of 974, 825 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 825 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 825 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.