Highest Common Factor of 160, 222 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, 222 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 160, 222 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, 222 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, 222 is 2.
HCF(160, 222) = 2
HCF of 160, 222 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, 222 is 2.
Highest Common Factor of 160,222 is 2
Step 1: Since 222 > 160, we apply the division lemma to 222 and 160, to get
222 = 160 x 1 + 62
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 62 and 160, to get
160 = 62 x 2 + 36
Step 3: We consider the new divisor 62 and the new remainder 36, and apply the division lemma to get
62 = 36 x 1 + 26
We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get
36 = 26 x 1 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 160 and 222 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(62,36) = HCF(160,62) = HCF(222,160) .
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Frequently Asked Questions on HCF of 160, 222 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, 222?
Answer: HCF of 160, 222 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 160, 222 using Euclid's Algorithm?
Answer: For arbitrary numbers 160, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.