Highest Common Factor of 21, 74, 260, 304 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, 74, 260, 304 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 21, 74, 260, 304 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, 74, 260, 304 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, 74, 260, 304 is 1.
HCF(21, 74, 260, 304) = 1
HCF of 21, 74, 260, 304 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, 74, 260, 304 is 1.
Highest Common Factor of 21,74,260,304 is 1
Step 1: Since 74 > 21, we apply the division lemma to 74 and 21, to get
74 = 21 x 3 + 11
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 11 and 21, to get
21 = 11 x 1 + 10
Step 3: We consider the new divisor 11 and the new remainder 10, and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1, and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 74 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(74,21) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 260 > 1, we apply the division lemma to 260 and 1, to get
260 = 1 x 260 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 260 is 1
Notice that 1 = HCF(260,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 304 > 1, we apply the division lemma to 304 and 1, to get
304 = 1 x 304 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 304 is 1
Notice that 1 = HCF(304,1) .
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Frequently Asked Questions on HCF of 21, 74, 260, 304 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, 74, 260, 304?
Answer: HCF of 21, 74, 260, 304 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 21, 74, 260, 304 using Euclid's Algorithm?
Answer: For arbitrary numbers 21, 74, 260, 304 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.