Highest Common Factor of 459, 753, 962 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 459, 753, 962 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 753, 962 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 459, 753, 962 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 459, 753, 962 is 1.
HCF(459, 753, 962) = 1
HCF of 459, 753, 962 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 459, 753, 962 is 1.
Highest Common Factor of 459,753,962 is 1
Step 1: Since 753 > 459, we apply the division lemma to 753 and 459, to get
753 = 459 x 1 + 294
Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 294 and 459, to get
459 = 294 x 1 + 165
Step 3: We consider the new divisor 294 and the new remainder 165, and apply the division lemma to get
294 = 165 x 1 + 129
We consider the new divisor 165 and the new remainder 129,and apply the division lemma to get
165 = 129 x 1 + 36
We consider the new divisor 129 and the new remainder 36,and apply the division lemma to get
129 = 36 x 3 + 21
We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 459 and 753 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(129,36) = HCF(165,129) = HCF(294,165) = HCF(459,294) = HCF(753,459) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 962 > 3, we apply the division lemma to 962 and 3, to get
962 = 3 x 320 + 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 962 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(962,3) .
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Frequently Asked Questions on HCF of 459, 753, 962 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 459, 753, 962?
Answer: HCF of 459, 753, 962 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 753, 962 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 753, 962 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
