Highest Common Factor of 121, 223, 74 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 121, 223, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 121, 223, 74 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 121, 223, 74 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 121, 223, 74 is 1.
HCF(121, 223, 74) = 1
HCF of 121, 223, 74 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 121, 223, 74 is 1.
Highest Common Factor of 121,223,74 is 1
Step 1: Since 223 > 121, we apply the division lemma to 223 and 121, to get
223 = 121 x 1 + 102
Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 102 and 121, to get
121 = 102 x 1 + 19
Step 3: We consider the new divisor 102 and the new remainder 19, and apply the division lemma to get
102 = 19 x 5 + 7
We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get
19 = 7 x 2 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 121 and 223 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(102,19) = HCF(121,102) = HCF(223,121) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get
74 = 1 x 74 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1
Notice that 1 = HCF(74,1) .
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Frequently Asked Questions on HCF of 121, 223, 74 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 121, 223, 74?
Answer: HCF of 121, 223, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 121, 223, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 121, 223, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.