Highest Common Factor of 829, 970 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 829, 970 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 829, 970 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 829, 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 829, 970 is 1.
HCF(829, 970) = 1
HCF of 829, 970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 829, 970 is 1.
Highest Common Factor of 829,970 is 1
Step 1: Since 970 > 829, we apply the division lemma to 970 and 829, to get
970 = 829 x 1 + 141
Step 2: Since the reminder 829 ≠ 0, we apply division lemma to 141 and 829, to get
829 = 141 x 5 + 124
Step 3: We consider the new divisor 141 and the new remainder 124, and apply the division lemma to get
141 = 124 x 1 + 17
We consider the new divisor 124 and the new remainder 17,and apply the division lemma to get
124 = 17 x 7 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 829 and 970 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(124,17) = HCF(141,124) = HCF(829,141) = HCF(970,829) .
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Frequently Asked Questions on HCF of 829, 970 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 829, 970?
Answer: HCF of 829, 970 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 829, 970 using Euclid's Algorithm?
Answer: For arbitrary numbers 829, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.