Highest Common Factor of 7064, 8400 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 7064, 8400 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 7064, 8400 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 7064, 8400 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 7064, 8400 is 8.
HCF(7064, 8400) = 8
HCF of 7064, 8400 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7064, 8400 is 8.
Highest Common Factor of 7064,8400 is 8
Step 1: Since 8400 > 7064, we apply the division lemma to 8400 and 7064, to get
8400 = 7064 x 1 + 1336
Step 2: Since the reminder 7064 ≠ 0, we apply division lemma to 1336 and 7064, to get
7064 = 1336 x 5 + 384
Step 3: We consider the new divisor 1336 and the new remainder 384, and apply the division lemma to get
1336 = 384 x 3 + 184
We consider the new divisor 384 and the new remainder 184,and apply the division lemma to get
384 = 184 x 2 + 16
We consider the new divisor 184 and the new remainder 16,and apply the division lemma to get
184 = 16 x 11 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 7064 and 8400 is 8
Notice that 8 = HCF(16,8) = HCF(184,16) = HCF(384,184) = HCF(1336,384) = HCF(7064,1336) = HCF(8400,7064) .
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Frequently Asked Questions on HCF of 7064, 8400 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 7064, 8400?
Answer: HCF of 7064, 8400 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7064, 8400 using Euclid's Algorithm?
Answer: For arbitrary numbers 7064, 8400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.