Highest Common Factor of 160, 442, 446 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 160, 442, 446 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 160, 442, 446 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 160, 442, 446 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 160, 442, 446 is 2.
HCF(160, 442, 446) = 2
HCF of 160, 442, 446 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 160, 442, 446 is 2.
Highest Common Factor of 160,442,446 is 2
Step 1: Since 442 > 160, we apply the division lemma to 442 and 160, to get
442 = 160 x 2 + 122
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 122 and 160, to get
160 = 122 x 1 + 38
Step 3: We consider the new divisor 122 and the new remainder 38, and apply the division lemma to get
122 = 38 x 3 + 8
We consider the new divisor 38 and the new remainder 8,and apply the division lemma to get
38 = 8 x 4 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 160 and 442 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(122,38) = HCF(160,122) = HCF(442,160) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 446 > 2, we apply the division lemma to 446 and 2, to get
446 = 2 x 223 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 446 is 2
Notice that 2 = HCF(446,2) .
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Frequently Asked Questions on HCF of 160, 442, 446 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 160, 442, 446?
Answer: HCF of 160, 442, 446 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 160, 442, 446 using Euclid's Algorithm?
Answer: For arbitrary numbers 160, 442, 446 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.