Highest Common Factor of 24, 108, 105 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 24, 108, 105 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 24, 108, 105 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 24, 108, 105 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 24, 108, 105 is 3.
HCF(24, 108, 105) = 3
HCF of 24, 108, 105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 24, 108, 105 is 3.
Highest Common Factor of 24,108,105 is 3
Step 1: Since 108 > 24, we apply the division lemma to 108 and 24, to get
108 = 24 x 4 + 12
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 12 and 24, to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 24 and 108 is 12
Notice that 12 = HCF(24,12) = HCF(108,24) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 12, we apply the division lemma to 105 and 12, to get
105 = 12 x 8 + 9
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 9 and 12, to get
12 = 9 x 1 + 3
Step 3: We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 12 and 105 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(105,12) .
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Frequently Asked Questions on HCF of 24, 108, 105 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 24, 108, 105?
Answer: HCF of 24, 108, 105 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 24, 108, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 24, 108, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.