Highest Common Factor of 422, 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 422, 960 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 422, 960 is 2 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 422, 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 422, 960 is 2.
HCF(422, 960) = 2
HCF of 422, 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 422, 960 is 2.
Highest Common Factor of 422,960 is 2
Step 1: Since 960 > 422, we apply the division lemma to 960 and 422, to get
960 = 422 x 2 + 116
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 116 and 422, to get
422 = 116 x 3 + 74
Step 3: We consider the new divisor 116 and the new remainder 74, and apply the division lemma to get
116 = 74 x 1 + 42
We consider the new divisor 74 and the new remainder 42,and apply the division lemma to get
74 = 42 x 1 + 32
We consider the new divisor 42 and the new remainder 32,and apply the division lemma to get
42 = 32 x 1 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 422 and 960 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(74,42) = HCF(116,74) = HCF(422,116) = HCF(960,422) .
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Frequently Asked Questions on HCF of 422, 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 422, 960?
Answer: HCF of 422, 960 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 422, 960 using Euclid's Algorithm?
Answer: For arbitrary numbers 422, 960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.