Highest Common Factor of 988, 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 988, 724 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 724 is 4 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 988, 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 988, 724 is 4.
HCF(988, 724) = 4
HCF of 988, 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 988, 724 is 4.
Highest Common Factor of 988,724 is 4
Step 1: Since 988 > 724, we apply the division lemma to 988 and 724, to get
988 = 724 x 1 + 264
Step 2: Since the reminder 724 ≠ 0, we apply division lemma to 264 and 724, to get
724 = 264 x 2 + 196
Step 3: We consider the new divisor 264 and the new remainder 196, and apply the division lemma to get
264 = 196 x 1 + 68
We consider the new divisor 196 and the new remainder 68,and apply the division lemma to get
196 = 68 x 2 + 60
We consider the new divisor 68 and the new remainder 60,and apply the division lemma to get
68 = 60 x 1 + 8
We consider the new divisor 60 and the new remainder 8,and apply the division lemma to get
60 = 8 x 7 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 988 and 724 is 4
Notice that 4 = HCF(8,4) = HCF(60,8) = HCF(68,60) = HCF(196,68) = HCF(264,196) = HCF(724,264) = HCF(988,724) .
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Frequently Asked Questions on HCF of 988, 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 988, 724?
Answer: HCF of 988, 724 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 724 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.