Highest Common Factor of 322, 874, 32 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 322, 874, 32 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 322, 874, 32 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 322, 874, 32 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 322, 874, 32 is 2.
HCF(322, 874, 32) = 2
HCF of 322, 874, 32 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 322, 874, 32 is 2.
Highest Common Factor of 322,874,32 is 2
Step 1: Since 874 > 322, we apply the division lemma to 874 and 322, to get
874 = 322 x 2 + 230
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 230 and 322, to get
322 = 230 x 1 + 92
Step 3: We consider the new divisor 230 and the new remainder 92, and apply the division lemma to get
230 = 92 x 2 + 46
We consider the new divisor 92 and the new remainder 46, and apply the division lemma to get
92 = 46 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 46, the HCF of 322 and 874 is 46
Notice that 46 = HCF(92,46) = HCF(230,92) = HCF(322,230) = HCF(874,322) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 46 > 32, we apply the division lemma to 46 and 32, to get
46 = 32 x 1 + 14
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 14 and 32, to get
32 = 14 x 2 + 4
Step 3: We consider the new divisor 14 and the new remainder 4, and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 46 and 32 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(46,32) .
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Frequently Asked Questions on HCF of 322, 874, 32 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 322, 874, 32?
Answer: HCF of 322, 874, 32 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 322, 874, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 322, 874, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.