Highest Common Factor of 370, 144, 149 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 370, 144, 149 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 370, 144, 149 is 1 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 370, 144, 149 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 370, 144, 149 is 1.
HCF(370, 144, 149) = 1
HCF of 370, 144, 149 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 370, 144, 149 is 1.
Highest Common Factor of 370,144,149 is 1
Step 1: Since 370 > 144, we apply the division lemma to 370 and 144, to get
370 = 144 x 2 + 82
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 82 and 144, to get
144 = 82 x 1 + 62
Step 3: We consider the new divisor 82 and the new remainder 62, and apply the division lemma to get
82 = 62 x 1 + 20
We consider the new divisor 62 and the new remainder 20,and apply the division lemma to get
62 = 20 x 3 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 370 and 144 is 2
Notice that 2 = HCF(20,2) = HCF(62,20) = HCF(82,62) = HCF(144,82) = HCF(370,144) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 149 > 2, we apply the division lemma to 149 and 2, to get
149 = 2 x 74 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 149 is 1
Notice that 1 = HCF(2,1) = HCF(149,2) .
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Frequently Asked Questions on HCF of 370, 144, 149 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 370, 144, 149?
Answer: HCF of 370, 144, 149 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 370, 144, 149 using Euclid's Algorithm?
Answer: For arbitrary numbers 370, 144, 149 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.