Highest Common Factor of 724, 7004 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 724, 7004 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 724, 7004 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 724, 7004 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 724, 7004 is 4.
HCF(724, 7004) = 4
HCF of 724, 7004 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 724, 7004 is 4.
Highest Common Factor of 724,7004 is 4
Step 1: Since 7004 > 724, we apply the division lemma to 7004 and 724, to get
7004 = 724 x 9 + 488
Step 2: Since the reminder 724 ≠ 0, we apply division lemma to 488 and 724, to get
724 = 488 x 1 + 236
Step 3: We consider the new divisor 488 and the new remainder 236, and apply the division lemma to get
488 = 236 x 2 + 16
We consider the new divisor 236 and the new remainder 16,and apply the division lemma to get
236 = 16 x 14 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 724 and 7004 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(236,16) = HCF(488,236) = HCF(724,488) = HCF(7004,724) .
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Frequently Asked Questions on HCF of 724, 7004 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 724, 7004?
Answer: HCF of 724, 7004 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 724, 7004 using Euclid's Algorithm?
Answer: For arbitrary numbers 724, 7004 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.