Highest Common Factor of 144, 961, 37 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 144, 961, 37 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 144, 961, 37 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 144, 961, 37 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 144, 961, 37 is 1.
HCF(144, 961, 37) = 1
HCF of 144, 961, 37 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 144, 961, 37 is 1.
Highest Common Factor of 144,961,37 is 1
Step 1: Since 961 > 144, we apply the division lemma to 961 and 144, to get
961 = 144 x 6 + 97
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 97 and 144, to get
144 = 97 x 1 + 47
Step 3: We consider the new divisor 97 and the new remainder 47, and apply the division lemma to get
97 = 47 x 2 + 3
We consider the new divisor 47 and the new remainder 3,and apply the division lemma to get
47 = 3 x 15 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 144 and 961 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(47,3) = HCF(97,47) = HCF(144,97) = HCF(961,144) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 37 > 1, we apply the division lemma to 37 and 1, to get
37 = 1 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 37 is 1
Notice that 1 = HCF(37,1) .
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Frequently Asked Questions on HCF of 144, 961, 37 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 144, 961, 37?
Answer: HCF of 144, 961, 37 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 144, 961, 37 using Euclid's Algorithm?
Answer: For arbitrary numbers 144, 961, 37 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.