Highest Common Factor of 999, 768, 653, 64 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, 768, 653, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 999, 768, 653, 64 is 1 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, 768, 653, 64 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, 768, 653, 64 is 1.
HCF(999, 768, 653, 64) = 1
HCF of 999, 768, 653, 64 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, 768, 653, 64 is 1.
Highest Common Factor of 999,768,653,64 is 1
Step 1: Since 999 > 768, we apply the division lemma to 999 and 768, to get
999 = 768 x 1 + 231
Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 231 and 768, to get
768 = 231 x 3 + 75
Step 3: We consider the new divisor 231 and the new remainder 75, and apply the division lemma to get
231 = 75 x 3 + 6
We consider the new divisor 75 and the new remainder 6,and apply the division lemma to get
75 = 6 x 12 + 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 768 is 3
Notice that 3 = HCF(6,3) = HCF(75,6) = HCF(231,75) = HCF(768,231) = HCF(999,768) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 653 > 3, we apply the division lemma to 653 and 3, to get
653 = 3 x 217 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 653 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(653,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 64 > 1, we apply the division lemma to 64 and 1, to get
64 = 1 x 64 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64 is 1
Notice that 1 = HCF(64,1) .
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Frequently Asked Questions on HCF of 999, 768, 653, 64 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, 768, 653, 64?
Answer: HCF of 999, 768, 653, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 999, 768, 653, 64 using Euclid's Algorithm?
Answer: For arbitrary numbers 999, 768, 653, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.