Highest Common Factor of 372, 579, 105 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, 579, 105 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 579, 105 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, 579, 105 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, 579, 105 is 3.
HCF(372, 579, 105) = 3
HCF of 372, 579, 105 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, 579, 105 is 3.
Highest Common Factor of 372,579,105 is 3
Step 1: Since 579 > 372, we apply the division lemma to 579 and 372, to get
579 = 372 x 1 + 207
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 207 and 372, to get
372 = 207 x 1 + 165
Step 3: We consider the new divisor 207 and the new remainder 165, and apply the division lemma to get
207 = 165 x 1 + 42
We consider the new divisor 165 and the new remainder 42,and apply the division lemma to get
165 = 42 x 3 + 39
We consider the new divisor 42 and the new remainder 39,and apply the division lemma to get
42 = 39 x 1 + 3
We consider the new divisor 39 and the new remainder 3,and apply the division lemma to get
39 = 3 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 372 and 579 is 3
Notice that 3 = HCF(39,3) = HCF(42,39) = HCF(165,42) = HCF(207,165) = HCF(372,207) = HCF(579,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 3, we apply the division lemma to 105 and 3, to get
105 = 3 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 105 is 3
Notice that 3 = HCF(105,3) .
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Frequently Asked Questions on HCF of 372, 579, 105 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, 579, 105?
Answer: HCF of 372, 579, 105 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 579, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 579, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.