Highest Common Factor of 448, 728, 765, 39 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 448, 728, 765, 39 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 728, 765, 39 is 1 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 448, 728, 765, 39 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 448, 728, 765, 39 is 1.
HCF(448, 728, 765, 39) = 1
HCF of 448, 728, 765, 39 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 728, 765, 39 is 1.
Highest Common Factor of 448,728,765,39 is 1
Step 1: Since 728 > 448, we apply the division lemma to 728 and 448, to get
728 = 448 x 1 + 280
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 280 and 448, to get
448 = 280 x 1 + 168
Step 3: We consider the new divisor 280 and the new remainder 168, and apply the division lemma to get
280 = 168 x 1 + 112
We consider the new divisor 168 and the new remainder 112,and apply the division lemma to get
168 = 112 x 1 + 56
We consider the new divisor 112 and the new remainder 56,and apply the division lemma to get
112 = 56 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 56, the HCF of 448 and 728 is 56
Notice that 56 = HCF(112,56) = HCF(168,112) = HCF(280,168) = HCF(448,280) = HCF(728,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 765 > 56, we apply the division lemma to 765 and 56, to get
765 = 56 x 13 + 37
Step 2: Since the reminder 56 ≠ 0, we apply division lemma to 37 and 56, to get
56 = 37 x 1 + 19
Step 3: We consider the new divisor 37 and the new remainder 19, and apply the division lemma to get
37 = 19 x 1 + 18
We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get
19 = 18 x 1 + 1
We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get
18 = 1 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 56 and 765 is 1
Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(56,37) = HCF(765,56) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 39 > 1, we apply the division lemma to 39 and 1, to get
39 = 1 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 39 is 1
Notice that 1 = HCF(39,1) .
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Frequently Asked Questions on HCF of 448, 728, 765, 39 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 448, 728, 765, 39?
Answer: HCF of 448, 728, 765, 39 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 728, 765, 39 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 728, 765, 39 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.