Highest Common Factor of 633, 960 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 633, 960 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 633, 960 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 633, 960 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 633, 960 is 3.
HCF(633, 960) = 3
HCF of 633, 960 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 633, 960 is 3.
Highest Common Factor of 633,960 is 3
Step 1: Since 960 > 633, we apply the division lemma to 960 and 633, to get
960 = 633 x 1 + 327
Step 2: Since the reminder 633 ≠ 0, we apply division lemma to 327 and 633, to get
633 = 327 x 1 + 306
Step 3: We consider the new divisor 327 and the new remainder 306, and apply the division lemma to get
327 = 306 x 1 + 21
We consider the new divisor 306 and the new remainder 21,and apply the division lemma to get
306 = 21 x 14 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 633 and 960 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(306,21) = HCF(327,306) = HCF(633,327) = HCF(960,633) .
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Frequently Asked Questions on HCF of 633, 960 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 633, 960?
Answer: HCF of 633, 960 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 633, 960 using Euclid's Algorithm?
Answer: For arbitrary numbers 633, 960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.