Highest Common Factor of 999, 732, 678 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, 732, 678 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 999, 732, 678 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 999, 732, 678 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, 732, 678 is 3.
HCF(999, 732, 678) = 3
HCF of 999, 732, 678 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, 732, 678 is 3.
Highest Common Factor of 999,732,678 is 3
Step 1: Since 999 > 732, we apply the division lemma to 999 and 732, to get
999 = 732 x 1 + 267
Step 2: Since the reminder 732 ≠ 0, we apply division lemma to 267 and 732, to get
732 = 267 x 2 + 198
Step 3: We consider the new divisor 267 and the new remainder 198, and apply the division lemma to get
267 = 198 x 1 + 69
We consider the new divisor 198 and the new remainder 69,and apply the division lemma to get
198 = 69 x 2 + 60
We consider the new divisor 69 and the new remainder 60,and apply the division lemma to get
69 = 60 x 1 + 9
We consider the new divisor 60 and the new remainder 9,and apply the division lemma to get
60 = 9 x 6 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 999 and 732 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) = HCF(69,60) = HCF(198,69) = HCF(267,198) = HCF(732,267) = HCF(999,732) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 3, we apply the division lemma to 678 and 3, to get
678 = 3 x 226 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 678 is 3
Notice that 3 = HCF(678,3) .
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Frequently Asked Questions on HCF of 999, 732, 678 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, 732, 678?
Answer: HCF of 999, 732, 678 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 999, 732, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 999, 732, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
