Highest Common Factor of 372, 138, 597 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 372, 138, 597 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 138, 597 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 372, 138, 597 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 372, 138, 597 is 3.
HCF(372, 138, 597) = 3
HCF of 372, 138, 597 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 372, 138, 597 is 3.
Highest Common Factor of 372,138,597 is 3
Step 1: Since 372 > 138, we apply the division lemma to 372 and 138, to get
372 = 138 x 2 + 96
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 96 and 138, to get
138 = 96 x 1 + 42
Step 3: We consider the new divisor 96 and the new remainder 42, and apply the division lemma to get
96 = 42 x 2 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 372 and 138 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(96,42) = HCF(138,96) = HCF(372,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 597 > 6, we apply the division lemma to 597 and 6, to get
597 = 6 x 99 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, 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 6 and 597 is 3
Notice that 3 = HCF(6,3) = HCF(597,6) .
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Frequently Asked Questions on HCF of 372, 138, 597 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 372, 138, 597?
Answer: HCF of 372, 138, 597 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 138, 597 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 138, 597 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.