Highest Common Factor of 792, 459, 888 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, 459, 888 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 792, 459, 888 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, 459, 888 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, 459, 888 is 3.
HCF(792, 459, 888) = 3
HCF of 792, 459, 888 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, 459, 888 is 3.
Highest Common Factor of 792,459,888 is 3
Step 1: Since 792 > 459, we apply the division lemma to 792 and 459, to get
792 = 459 x 1 + 333
Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 333 and 459, to get
459 = 333 x 1 + 126
Step 3: We consider the new divisor 333 and the new remainder 126, and apply the division lemma to get
333 = 126 x 2 + 81
We consider the new divisor 126 and the new remainder 81,and apply the division lemma to get
126 = 81 x 1 + 45
We consider the new divisor 81 and the new remainder 45,and apply the division lemma to get
81 = 45 x 1 + 36
We consider the new divisor 45 and the new remainder 36,and apply the division lemma to get
45 = 36 x 1 + 9
We consider the new divisor 36 and the new remainder 9,and apply the division lemma to get
36 = 9 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 792 and 459 is 9
Notice that 9 = HCF(36,9) = HCF(45,36) = HCF(81,45) = HCF(126,81) = HCF(333,126) = HCF(459,333) = HCF(792,459) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 888 > 9, we apply the division lemma to 888 and 9, to get
888 = 9 x 98 + 6
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get
9 = 6 x 1 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma 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 9 and 888 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(888,9) .
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Frequently Asked Questions on HCF of 792, 459, 888 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, 459, 888?
Answer: HCF of 792, 459, 888 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 792, 459, 888 using Euclid's Algorithm?
Answer: For arbitrary numbers 792, 459, 888 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.