Highest Common Factor of 8304, 9772 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 8304, 9772 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 8304, 9772 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 8304, 9772 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 8304, 9772 is 4.
HCF(8304, 9772) = 4
HCF of 8304, 9772 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8304, 9772 is 4.
Highest Common Factor of 8304,9772 is 4
Step 1: Since 9772 > 8304, we apply the division lemma to 9772 and 8304, to get
9772 = 8304 x 1 + 1468
Step 2: Since the reminder 8304 ≠ 0, we apply division lemma to 1468 and 8304, to get
8304 = 1468 x 5 + 964
Step 3: We consider the new divisor 1468 and the new remainder 964, and apply the division lemma to get
1468 = 964 x 1 + 504
We consider the new divisor 964 and the new remainder 504,and apply the division lemma to get
964 = 504 x 1 + 460
We consider the new divisor 504 and the new remainder 460,and apply the division lemma to get
504 = 460 x 1 + 44
We consider the new divisor 460 and the new remainder 44,and apply the division lemma to get
460 = 44 x 10 + 20
We consider the new divisor 44 and the new remainder 20,and apply the division lemma to get
44 = 20 x 2 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8304 and 9772 is 4
Notice that 4 = HCF(20,4) = HCF(44,20) = HCF(460,44) = HCF(504,460) = HCF(964,504) = HCF(1468,964) = HCF(8304,1468) = HCF(9772,8304) .
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Frequently Asked Questions on HCF of 8304, 9772 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 8304, 9772?
Answer: HCF of 8304, 9772 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8304, 9772 using Euclid's Algorithm?
Answer: For arbitrary numbers 8304, 9772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.