Highest Common Factor of 999, 594, 144 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 999, 594, 144 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 999, 594, 144 is 9 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 999, 594, 144 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 999, 594, 144 is 9.
HCF(999, 594, 144) = 9
HCF of 999, 594, 144 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 999, 594, 144 is 9.
Highest Common Factor of 999,594,144 is 9
Step 1: Since 999 > 594, we apply the division lemma to 999 and 594, to get
999 = 594 x 1 + 405
Step 2: Since the reminder 594 ≠ 0, we apply division lemma to 405 and 594, to get
594 = 405 x 1 + 189
Step 3: We consider the new divisor 405 and the new remainder 189, and apply the division lemma to get
405 = 189 x 2 + 27
We consider the new divisor 189 and the new remainder 27, and apply the division lemma to get
189 = 27 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 999 and 594 is 27
Notice that 27 = HCF(189,27) = HCF(405,189) = HCF(594,405) = HCF(999,594) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 144 > 27, we apply the division lemma to 144 and 27, to get
144 = 27 x 5 + 9
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 9 and 27, to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 27 and 144 is 9
Notice that 9 = HCF(27,9) = HCF(144,27) .
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Frequently Asked Questions on HCF of 999, 594, 144 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 999, 594, 144?
Answer: HCF of 999, 594, 144 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 999, 594, 144 using Euclid's Algorithm?
Answer: For arbitrary numbers 999, 594, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.