Highest Common Factor of 768, 552, 902 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 768, 552, 902 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 552, 902 is 2 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, 552, 902 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, 552, 902 is 2.
HCF(768, 552, 902) = 2
HCF of 768, 552, 902 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 552, 902 is 2.
Highest Common Factor of 768,552,902 is 2
Step 1: Since 768 > 552, we apply the division lemma to 768 and 552, to get
768 = 552 x 1 + 216
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 216 and 552, to get
552 = 216 x 2 + 120
Step 3: We consider the new divisor 216 and the new remainder 120, and apply the division lemma to get
216 = 120 x 1 + 96
We consider the new divisor 120 and the new remainder 96,and apply the division lemma to get
120 = 96 x 1 + 24
We consider the new divisor 96 and the new remainder 24,and apply the division lemma to get
96 = 24 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 768 and 552 is 24
Notice that 24 = HCF(96,24) = HCF(120,96) = HCF(216,120) = HCF(552,216) = HCF(768,552) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 902 > 24, we apply the division lemma to 902 and 24, to get
902 = 24 x 37 + 14
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 14 and 24, to get
24 = 14 x 1 + 10
Step 3: We consider the new divisor 14 and the new remainder 10, and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 24 and 902 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(902,24) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 768, 552, 902 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 768, 552, 902?
Answer: HCF of 768, 552, 902 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 552, 902 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 552, 902 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.