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 768, 440, 517, 33 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 440, 517, 33 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 768, 440, 517, 33 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 768, 440, 517, 33 is 1.
HCF(768, 440, 517, 33) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 440, 517, 33 is 1.
Step 1: Since 768 > 440, we apply the division lemma to 768 and 440, to get
768 = 440 x 1 + 328
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 328 and 440, to get
440 = 328 x 1 + 112
Step 3: We consider the new divisor 328 and the new remainder 112, and apply the division lemma to get
328 = 112 x 2 + 104
We consider the new divisor 112 and the new remainder 104,and apply the division lemma to get
112 = 104 x 1 + 8
We consider the new divisor 104 and the new remainder 8,and apply the division lemma to get
104 = 8 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 768 and 440 is 8
Notice that 8 = HCF(104,8) = HCF(112,104) = HCF(328,112) = HCF(440,328) = HCF(768,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 517 > 8, we apply the division lemma to 517 and 8, to get
517 = 8 x 64 + 5
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get
8 = 5 x 1 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 8 and 517 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(517,8) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 33 > 1, we apply the division lemma to 33 and 1, to get
33 = 1 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 33 is 1
Notice that 1 = HCF(33,1) .
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 768, 440, 517, 33?
Answer: HCF of 768, 440, 517, 33 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 440, 517, 33 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 440, 517, 33 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.