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, 443, 548, 24 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 443, 548, 24 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 765, 443, 548, 24 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, 443, 548, 24 is 1.
HCF(765, 443, 548, 24) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 765, 443, 548, 24 is 1.
Step 1: Since 765 > 443, we apply the division lemma to 765 and 443, to get
765 = 443 x 1 + 322
Step 2: Since the reminder 443 ≠ 0, we apply division lemma to 322 and 443, to get
443 = 322 x 1 + 121
Step 3: We consider the new divisor 322 and the new remainder 121, and apply the division lemma to get
322 = 121 x 2 + 80
We consider the new divisor 121 and the new remainder 80,and apply the division lemma to get
121 = 80 x 1 + 41
We consider the new divisor 80 and the new remainder 41,and apply the division lemma to get
80 = 41 x 1 + 39
We consider the new divisor 41 and the new remainder 39,and apply the division lemma to get
41 = 39 x 1 + 2
We consider the new divisor 39 and the new remainder 2,and apply the division lemma to get
39 = 2 x 19 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 765 and 443 is 1
Notice that 1 = HCF(2,1) = HCF(39,2) = HCF(41,39) = HCF(80,41) = HCF(121,80) = HCF(322,121) = HCF(443,322) = HCF(765,443) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 548 > 1, we apply the division lemma to 548 and 1, to get
548 = 1 x 548 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 548 is 1
Notice that 1 = HCF(548,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 24 > 1, we apply the division lemma to 24 and 1, to get
24 = 1 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 24 is 1
Notice that 1 = HCF(24,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 443, 548, 24?
Answer: HCF of 765, 443, 548, 24 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 443, 548, 24 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 443, 548, 24 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.