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, 553, 47 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 553, 47 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, 553, 47 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, 553, 47 is 1.
HCF(765, 553, 47) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 765, 553, 47 is 1.
Step 1: Since 765 > 553, we apply the division lemma to 765 and 553, to get
765 = 553 x 1 + 212
Step 2: Since the reminder 553 ≠ 0, we apply division lemma to 212 and 553, to get
553 = 212 x 2 + 129
Step 3: We consider the new divisor 212 and the new remainder 129, and apply the division lemma to get
212 = 129 x 1 + 83
We consider the new divisor 129 and the new remainder 83,and apply the division lemma to get
129 = 83 x 1 + 46
We consider the new divisor 83 and the new remainder 46,and apply the division lemma to get
83 = 46 x 1 + 37
We consider the new divisor 46 and the new remainder 37,and apply the division lemma to get
46 = 37 x 1 + 9
We consider the new divisor 37 and the new remainder 9,and apply the division lemma to get
37 = 9 x 4 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 765 and 553 is 1
Notice that 1 = HCF(9,1) = HCF(37,9) = HCF(46,37) = HCF(83,46) = HCF(129,83) = HCF(212,129) = HCF(553,212) = HCF(765,553) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 47 > 1, we apply the division lemma to 47 and 1, to get
47 = 1 x 47 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 47 is 1
Notice that 1 = HCF(47,1) .
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, 553, 47?
Answer: HCF of 765, 553, 47 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 553, 47 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 553, 47 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.