Highest Common Factor of 732, 264, 874 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 732, 264, 874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 732, 264, 874 is 2 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 732, 264, 874 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 732, 264, 874 is 2.
HCF(732, 264, 874) = 2
HCF of 732, 264, 874 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 732, 264, 874 is 2.
Highest Common Factor of 732,264,874 is 2
Step 1: Since 732 > 264, we apply the division lemma to 732 and 264, to get
732 = 264 x 2 + 204
Step 2: Since the reminder 264 ≠ 0, we apply division lemma to 204 and 264, to get
264 = 204 x 1 + 60
Step 3: We consider the new divisor 204 and the new remainder 60, and apply the division lemma to get
204 = 60 x 3 + 24
We consider the new divisor 60 and the new remainder 24,and apply the division lemma to get
60 = 24 x 2 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma 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 732 and 264 is 12
Notice that 12 = HCF(24,12) = HCF(60,24) = HCF(204,60) = HCF(264,204) = HCF(732,264) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 874 > 12, we apply the division lemma to 874 and 12, to get
874 = 12 x 72 + 10
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 10 and 12, to get
12 = 10 x 1 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 874 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(874,12) .
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Frequently Asked Questions on HCF of 732, 264, 874 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 732, 264, 874?
Answer: HCF of 732, 264, 874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 732, 264, 874 using Euclid's Algorithm?
Answer: For arbitrary numbers 732, 264, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.