Highest Common Factor of 765, 948, 345, 84 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 765, 948, 345, 84 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 948, 345, 84 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 765, 948, 345, 84 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 765, 948, 345, 84 is 3.
HCF(765, 948, 345, 84) = 3
HCF of 765, 948, 345, 84 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 765, 948, 345, 84 is 3.
Highest Common Factor of 765,948,345,84 is 3
Step 1: Since 948 > 765, we apply the division lemma to 948 and 765, to get
948 = 765 x 1 + 183
Step 2: Since the reminder 765 ≠ 0, we apply division lemma to 183 and 765, to get
765 = 183 x 4 + 33
Step 3: We consider the new divisor 183 and the new remainder 33, and apply the division lemma to get
183 = 33 x 5 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 765 and 948 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(183,33) = HCF(765,183) = HCF(948,765) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 345 > 3, we apply the division lemma to 345 and 3, to get
345 = 3 x 115 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 345 is 3
Notice that 3 = HCF(345,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 84 > 3, we apply the division lemma to 84 and 3, to get
84 = 3 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 84 is 3
Notice that 3 = HCF(84,3) .
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Frequently Asked Questions on HCF of 765, 948, 345, 84 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 765, 948, 345, 84?
Answer: HCF of 765, 948, 345, 84 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 948, 345, 84 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 948, 345, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.