Highest Common Factor of 7164, 8984 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 7164, 8984 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 7164, 8984 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 7164, 8984 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 7164, 8984 is 4.
HCF(7164, 8984) = 4
HCF of 7164, 8984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7164, 8984 is 4.
Highest Common Factor of 7164,8984 is 4
Step 1: Since 8984 > 7164, we apply the division lemma to 8984 and 7164, to get
8984 = 7164 x 1 + 1820
Step 2: Since the reminder 7164 ≠ 0, we apply division lemma to 1820 and 7164, to get
7164 = 1820 x 3 + 1704
Step 3: We consider the new divisor 1820 and the new remainder 1704, and apply the division lemma to get
1820 = 1704 x 1 + 116
We consider the new divisor 1704 and the new remainder 116,and apply the division lemma to get
1704 = 116 x 14 + 80
We consider the new divisor 116 and the new remainder 80,and apply the division lemma to get
116 = 80 x 1 + 36
We consider the new divisor 80 and the new remainder 36,and apply the division lemma to get
80 = 36 x 2 + 8
We consider the new divisor 36 and the new remainder 8,and apply the division lemma to get
36 = 8 x 4 + 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 7164 and 8984 is 4
Notice that 4 = HCF(8,4) = HCF(36,8) = HCF(80,36) = HCF(116,80) = HCF(1704,116) = HCF(1820,1704) = HCF(7164,1820) = HCF(8984,7164) .
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Frequently Asked Questions on HCF of 7164, 8984 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 7164, 8984?
Answer: HCF of 7164, 8984 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7164, 8984 using Euclid's Algorithm?
Answer: For arbitrary numbers 7164, 8984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
