Highest Common Factor of 306, 765, 372 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 306, 765, 372 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 765, 372 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 306, 765, 372 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 306, 765, 372 is 3.
HCF(306, 765, 372) = 3
HCF of 306, 765, 372 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 306, 765, 372 is 3.
Highest Common Factor of 306,765,372 is 3
Step 1: Since 765 > 306, we apply the division lemma to 765 and 306, to get
765 = 306 x 2 + 153
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 153 and 306, to get
306 = 153 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 153, the HCF of 306 and 765 is 153
Notice that 153 = HCF(306,153) = HCF(765,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 372 > 153, we apply the division lemma to 372 and 153, to get
372 = 153 x 2 + 66
Step 2: Since the reminder 153 ≠ 0, we apply division lemma to 66 and 153, to get
153 = 66 x 2 + 21
Step 3: We consider the new divisor 66 and the new remainder 21, and apply the division lemma to get
66 = 21 x 3 + 3
We consider the new divisor 21 and the new remainder 3, and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 153 and 372 is 3
Notice that 3 = HCF(21,3) = HCF(66,21) = HCF(153,66) = HCF(372,153) .
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Frequently Asked Questions on HCF of 306, 765, 372 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 306, 765, 372?
Answer: HCF of 306, 765, 372 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 765, 372 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 765, 372 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.