Highest Common Factor of 138, 375, 60 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 138, 375, 60 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 375, 60 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 138, 375, 60 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 138, 375, 60 is 3.
HCF(138, 375, 60) = 3
HCF of 138, 375, 60 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 138, 375, 60 is 3.
Highest Common Factor of 138,375,60 is 3
Step 1: Since 375 > 138, we apply the division lemma to 375 and 138, to get
375 = 138 x 2 + 99
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 99 and 138, to get
138 = 99 x 1 + 39
Step 3: 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 138 and 375 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(39,21) = HCF(99,39) = HCF(138,99) = HCF(375,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 3, we apply the division lemma to 60 and 3, to get
60 = 3 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 60 is 3
Notice that 3 = HCF(60,3) .
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Frequently Asked Questions on HCF of 138, 375, 60 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 138, 375, 60?
Answer: HCF of 138, 375, 60 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 375, 60 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 375, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.