Highest Common Factor of 237, 375, 332 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, 375, 332 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 237, 375, 332 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 237, 375, 332 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, 375, 332 is 1.
HCF(237, 375, 332) = 1
HCF of 237, 375, 332 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, 375, 332 is 1.
Highest Common Factor of 237,375,332 is 1
Step 1: Since 375 > 237, we apply the division lemma to 375 and 237, to get
375 = 237 x 1 + 138
Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 138 and 237, to get
237 = 138 x 1 + 99
Step 3: We consider the new divisor 138 and the new remainder 99, and apply the division lemma to get
138 = 99 x 1 + 39
We consider the new divisor 99 and the new remainder 39,and apply the division lemma to get
99 = 39 x 2 + 21
We consider the new divisor 39 and the new remainder 21,and apply the division lemma to get
39 = 21 x 1 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 237 and 375 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(39,21) = HCF(99,39) = HCF(138,99) = HCF(237,138) = HCF(375,237) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 332 > 3, we apply the division lemma to 332 and 3, to get
332 = 3 x 110 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 332 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(332,3) .
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Frequently Asked Questions on HCF of 237, 375, 332 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, 375, 332?
Answer: HCF of 237, 375, 332 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 237, 375, 332 using Euclid's Algorithm?
Answer: For arbitrary numbers 237, 375, 332 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.