Highest Common Factor of 21, 112, 123 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 21, 112, 123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 21, 112, 123 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 21, 112, 123 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 21, 112, 123 is 1.
HCF(21, 112, 123) = 1
HCF of 21, 112, 123 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 21, 112, 123 is 1.
Highest Common Factor of 21,112,123 is 1
Step 1: Since 112 > 21, we apply the division lemma to 112 and 21, to get
112 = 21 x 5 + 7
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 7 and 21, to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 21 and 112 is 7
Notice that 7 = HCF(21,7) = HCF(112,21) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 123 > 7, we apply the division lemma to 123 and 7, to get
123 = 7 x 17 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 123 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(123,7) .
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Frequently Asked Questions on HCF of 21, 112, 123 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 21, 112, 123?
Answer: HCF of 21, 112, 123 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 21, 112, 123 using Euclid's Algorithm?
Answer: For arbitrary numbers 21, 112, 123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.