Highest Common Factor of 160, 742, 190 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, 742, 190 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 160, 742, 190 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, 742, 190 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, 742, 190 is 2.
HCF(160, 742, 190) = 2
HCF of 160, 742, 190 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, 742, 190 is 2.
Highest Common Factor of 160,742,190 is 2
Step 1: Since 742 > 160, we apply the division lemma to 742 and 160, to get
742 = 160 x 4 + 102
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 102 and 160, to get
160 = 102 x 1 + 58
Step 3: We consider the new divisor 102 and the new remainder 58, and apply the division lemma to get
102 = 58 x 1 + 44
We consider the new divisor 58 and the new remainder 44,and apply the division lemma to get
58 = 44 x 1 + 14
We consider the new divisor 44 and the new remainder 14,and apply the division lemma to get
44 = 14 x 3 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 160 and 742 is 2
Notice that 2 = HCF(14,2) = HCF(44,14) = HCF(58,44) = HCF(102,58) = HCF(160,102) = HCF(742,160) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 190 > 2, we apply the division lemma to 190 and 2, to get
190 = 2 x 95 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 190 is 2
Notice that 2 = HCF(190,2) .
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Frequently Asked Questions on HCF of 160, 742, 190 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, 742, 190?
Answer: HCF of 160, 742, 190 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 160, 742, 190 using Euclid's Algorithm?
Answer: For arbitrary numbers 160, 742, 190 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.