Highest Common Factor of 989, 724 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 989, 724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 989, 724 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 989, 724 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 989, 724 is 1.
HCF(989, 724) = 1
HCF of 989, 724 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 989, 724 is 1.
Highest Common Factor of 989,724 is 1
Step 1: Since 989 > 724, we apply the division lemma to 989 and 724, to get
989 = 724 x 1 + 265
Step 2: Since the reminder 724 ≠ 0, we apply division lemma to 265 and 724, to get
724 = 265 x 2 + 194
Step 3: We consider the new divisor 265 and the new remainder 194, and apply the division lemma to get
265 = 194 x 1 + 71
We consider the new divisor 194 and the new remainder 71,and apply the division lemma to get
194 = 71 x 2 + 52
We consider the new divisor 71 and the new remainder 52,and apply the division lemma to get
71 = 52 x 1 + 19
We consider the new divisor 52 and the new remainder 19,and apply the division lemma to get
52 = 19 x 2 + 14
We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get
19 = 14 x 1 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 989 and 724 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(52,19) = HCF(71,52) = HCF(194,71) = HCF(265,194) = HCF(724,265) = HCF(989,724) .
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Frequently Asked Questions on HCF of 989, 724 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 989, 724?
Answer: HCF of 989, 724 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 989, 724 using Euclid's Algorithm?
Answer: For arbitrary numbers 989, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
