Highest Common Factor of 237, 144, 993 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 237, 144, 993 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 237, 144, 993 is 3 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 237, 144, 993 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 237, 144, 993 is 3.
HCF(237, 144, 993) = 3
HCF of 237, 144, 993 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 237, 144, 993 is 3.
Highest Common Factor of 237,144,993 is 3
Step 1: Since 237 > 144, we apply the division lemma to 237 and 144, to get
237 = 144 x 1 + 93
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 93 and 144, to get
144 = 93 x 1 + 51
Step 3: We consider the new divisor 93 and the new remainder 51, and apply the division lemma to get
93 = 51 x 1 + 42
We consider the new divisor 51 and the new remainder 42,and apply the division lemma to get
51 = 42 x 1 + 9
We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get
42 = 9 x 4 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 237 and 144 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(51,42) = HCF(93,51) = HCF(144,93) = HCF(237,144) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 993 > 3, we apply the division lemma to 993 and 3, to get
993 = 3 x 331 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 993 is 3
Notice that 3 = HCF(993,3) .
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Frequently Asked Questions on HCF of 237, 144, 993 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 237, 144, 993?
Answer: HCF of 237, 144, 993 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 237, 144, 993 using Euclid's Algorithm?
Answer: For arbitrary numbers 237, 144, 993 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
