Highest Common Factor of 7352, 6704 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 7352, 6704 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 7352, 6704 is 8 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 7352, 6704 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 7352, 6704 is 8.
HCF(7352, 6704) = 8
HCF of 7352, 6704 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7352, 6704 is 8.
Highest Common Factor of 7352,6704 is 8
Step 1: Since 7352 > 6704, we apply the division lemma to 7352 and 6704, to get
7352 = 6704 x 1 + 648
Step 2: Since the reminder 6704 ≠ 0, we apply division lemma to 648 and 6704, to get
6704 = 648 x 10 + 224
Step 3: We consider the new divisor 648 and the new remainder 224, and apply the division lemma to get
648 = 224 x 2 + 200
We consider the new divisor 224 and the new remainder 200,and apply the division lemma to get
224 = 200 x 1 + 24
We consider the new divisor 200 and the new remainder 24,and apply the division lemma to get
200 = 24 x 8 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 7352 and 6704 is 8
Notice that 8 = HCF(24,8) = HCF(200,24) = HCF(224,200) = HCF(648,224) = HCF(6704,648) = HCF(7352,6704) .
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Frequently Asked Questions on HCF of 7352, 6704 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 7352, 6704?
Answer: HCF of 7352, 6704 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7352, 6704 using Euclid's Algorithm?
Answer: For arbitrary numbers 7352, 6704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.