Highest Common Factor of 792, 498, 501 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 792, 498, 501 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 792, 498, 501 is 3 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 792, 498, 501 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 792, 498, 501 is 3.
HCF(792, 498, 501) = 3
HCF of 792, 498, 501 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 792, 498, 501 is 3.
Highest Common Factor of 792,498,501 is 3
Step 1: Since 792 > 498, we apply the division lemma to 792 and 498, to get
792 = 498 x 1 + 294
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 294 and 498, to get
498 = 294 x 1 + 204
Step 3: We consider the new divisor 294 and the new remainder 204, and apply the division lemma to get
294 = 204 x 1 + 90
We consider the new divisor 204 and the new remainder 90,and apply the division lemma to get
204 = 90 x 2 + 24
We consider the new divisor 90 and the new remainder 24,and apply the division lemma to get
90 = 24 x 3 + 18
We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 792 and 498 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(90,24) = HCF(204,90) = HCF(294,204) = HCF(498,294) = HCF(792,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 501 > 6, we apply the division lemma to 501 and 6, to get
501 = 6 x 83 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 501 is 3
Notice that 3 = HCF(6,3) = HCF(501,6) .
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Frequently Asked Questions on HCF of 792, 498, 501 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 792, 498, 501?
Answer: HCF of 792, 498, 501 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 792, 498, 501 using Euclid's Algorithm?
Answer: For arbitrary numbers 792, 498, 501 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.