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 9763, 7564, 54852 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9763, 7564, 54852 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 9763, 7564, 54852 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 9763, 7564, 54852 is 1.
HCF(9763, 7564, 54852) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9763, 7564, 54852 is 1.
Step 1: Since 9763 > 7564, we apply the division lemma to 9763 and 7564, to get
9763 = 7564 x 1 + 2199
Step 2: Since the reminder 7564 ≠ 0, we apply division lemma to 2199 and 7564, to get
7564 = 2199 x 3 + 967
Step 3: We consider the new divisor 2199 and the new remainder 967, and apply the division lemma to get
2199 = 967 x 2 + 265
We consider the new divisor 967 and the new remainder 265,and apply the division lemma to get
967 = 265 x 3 + 172
We consider the new divisor 265 and the new remainder 172,and apply the division lemma to get
265 = 172 x 1 + 93
We consider the new divisor 172 and the new remainder 93,and apply the division lemma to get
172 = 93 x 1 + 79
We consider the new divisor 93 and the new remainder 79,and apply the division lemma to get
93 = 79 x 1 + 14
We consider the new divisor 79 and the new remainder 14,and apply the division lemma to get
79 = 14 x 5 + 9
We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get
14 = 9 x 1 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9763 and 7564 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(79,14) = HCF(93,79) = HCF(172,93) = HCF(265,172) = HCF(967,265) = HCF(2199,967) = HCF(7564,2199) = HCF(9763,7564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54852 > 1, we apply the division lemma to 54852 and 1, to get
54852 = 1 x 54852 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 54852 is 1
Notice that 1 = HCF(54852,1) .
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 9763, 7564, 54852?
Answer: HCF of 9763, 7564, 54852 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9763, 7564, 54852 using Euclid's Algorithm?
Answer: For arbitrary numbers 9763, 7564, 54852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.