Highest Common Factor of 105, 924, 984 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 105, 924, 984 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 924, 984 is 3 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 105, 924, 984 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 105, 924, 984 is 3.
HCF(105, 924, 984) = 3
HCF of 105, 924, 984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 105, 924, 984 is 3.
Highest Common Factor of 105,924,984 is 3
Step 1: Since 924 > 105, we apply the division lemma to 924 and 105, to get
924 = 105 x 8 + 84
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 84 and 105, to get
105 = 84 x 1 + 21
Step 3: We consider the new divisor 84 and the new remainder 21, and apply the division lemma to get
84 = 21 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 105 and 924 is 21
Notice that 21 = HCF(84,21) = HCF(105,84) = HCF(924,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 984 > 21, we apply the division lemma to 984 and 21, to get
984 = 21 x 46 + 18
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 18 and 21, to get
21 = 18 x 1 + 3
Step 3: We consider the new divisor 18 and the new remainder 3, and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 984 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(984,21) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 105, 924, 984 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 105, 924, 984?
Answer: HCF of 105, 924, 984 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 924, 984 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 924, 984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.