Highest Common Factor of 3774, 9225, 34821 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 3774, 9225, 34821 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3774, 9225, 34821 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 3774, 9225, 34821 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 3774, 9225, 34821 is 3.
HCF(3774, 9225, 34821) = 3
HCF of 3774, 9225, 34821 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3774, 9225, 34821 is 3.
Highest Common Factor of 3774,9225,34821 is 3
Step 1: Since 9225 > 3774, we apply the division lemma to 9225 and 3774, to get
9225 = 3774 x 2 + 1677
Step 2: Since the reminder 3774 ≠ 0, we apply division lemma to 1677 and 3774, to get
3774 = 1677 x 2 + 420
Step 3: We consider the new divisor 1677 and the new remainder 420, and apply the division lemma to get
1677 = 420 x 3 + 417
We consider the new divisor 420 and the new remainder 417,and apply the division lemma to get
420 = 417 x 1 + 3
We consider the new divisor 417 and the new remainder 3,and apply the division lemma to get
417 = 3 x 139 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3774 and 9225 is 3
Notice that 3 = HCF(417,3) = HCF(420,417) = HCF(1677,420) = HCF(3774,1677) = HCF(9225,3774) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 34821 > 3, we apply the division lemma to 34821 and 3, to get
34821 = 3 x 11607 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 34821 is 3
Notice that 3 = HCF(34821,3) .
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Frequently Asked Questions on HCF of 3774, 9225, 34821 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 3774, 9225, 34821?
Answer: HCF of 3774, 9225, 34821 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3774, 9225, 34821 using Euclid's Algorithm?
Answer: For arbitrary numbers 3774, 9225, 34821 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.