Highest Common Factor of 456, 765, 144 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 456, 765, 144 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 456, 765, 144 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 456, 765, 144 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 456, 765, 144 is 3.
HCF(456, 765, 144) = 3
HCF of 456, 765, 144 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 456, 765, 144 is 3.
Highest Common Factor of 456,765,144 is 3
Step 1: Since 765 > 456, we apply the division lemma to 765 and 456, to get
765 = 456 x 1 + 309
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 309 and 456, to get
456 = 309 x 1 + 147
Step 3: We consider the new divisor 309 and the new remainder 147, and apply the division lemma to get
309 = 147 x 2 + 15
We consider the new divisor 147 and the new remainder 15,and apply the division lemma to get
147 = 15 x 9 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 456 and 765 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(147,15) = HCF(309,147) = HCF(456,309) = HCF(765,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 144 > 3, we apply the division lemma to 144 and 3, to get
144 = 3 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 144 is 3
Notice that 3 = HCF(144,3) .
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Frequently Asked Questions on HCF of 456, 765, 144 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 456, 765, 144?
Answer: HCF of 456, 765, 144 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 456, 765, 144 using Euclid's Algorithm?
Answer: For arbitrary numbers 456, 765, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.