Highest Common Factor of 984, 864, 904 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 984, 864, 904 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 984, 864, 904 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 984, 864, 904 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 984, 864, 904 is 8.
HCF(984, 864, 904) = 8
HCF of 984, 864, 904 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 984, 864, 904 is 8.
Highest Common Factor of 984,864,904 is 8
Step 1: Since 984 > 864, we apply the division lemma to 984 and 864, to get
984 = 864 x 1 + 120
Step 2: Since the reminder 864 ≠ 0, we apply division lemma to 120 and 864, to get
864 = 120 x 7 + 24
Step 3: We consider the new divisor 120 and the new remainder 24, and apply the division lemma to get
120 = 24 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 984 and 864 is 24
Notice that 24 = HCF(120,24) = HCF(864,120) = HCF(984,864) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 904 > 24, we apply the division lemma to 904 and 24, to get
904 = 24 x 37 + 16
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 16 and 24, to get
24 = 16 x 1 + 8
Step 3: 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 24 and 904 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(904,24) .
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Frequently Asked Questions on HCF of 984, 864, 904 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 984, 864, 904?
Answer: HCF of 984, 864, 904 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 984, 864, 904 using Euclid's Algorithm?
Answer: For arbitrary numbers 984, 864, 904 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.