Highest Common Factor of 992, 832, 504 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 992, 832, 504 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 992, 832, 504 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 992, 832, 504 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 992, 832, 504 is 8.
HCF(992, 832, 504) = 8
HCF of 992, 832, 504 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 992, 832, 504 is 8.
Highest Common Factor of 992,832,504 is 8
Step 1: Since 992 > 832, we apply the division lemma to 992 and 832, to get
992 = 832 x 1 + 160
Step 2: Since the reminder 832 ≠ 0, we apply division lemma to 160 and 832, to get
832 = 160 x 5 + 32
Step 3: We consider the new divisor 160 and the new remainder 32, and apply the division lemma to get
160 = 32 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 992 and 832 is 32
Notice that 32 = HCF(160,32) = HCF(832,160) = HCF(992,832) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 504 > 32, we apply the division lemma to 504 and 32, to get
504 = 32 x 15 + 24
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 24 and 32, to get
32 = 24 x 1 + 8
Step 3: 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 32 and 504 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(504,32) .
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Frequently Asked Questions on HCF of 992, 832, 504 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 992, 832, 504?
Answer: HCF of 992, 832, 504 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 992, 832, 504 using Euclid's Algorithm?
Answer: For arbitrary numbers 992, 832, 504 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
