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 978, 346, 32 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 346, 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 978, 346, 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 978, 346, 32 is 2.
HCF(978, 346, 32) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 346, 32 is 2.
Step 1: Since 978 > 346, we apply the division lemma to 978 and 346, to get
978 = 346 x 2 + 286
Step 2: Since the reminder 346 ≠ 0, we apply division lemma to 286 and 346, to get
346 = 286 x 1 + 60
Step 3: We consider the new divisor 286 and the new remainder 60, and apply the division lemma to get
286 = 60 x 4 + 46
We consider the new divisor 60 and the new remainder 46,and apply the division lemma to get
60 = 46 x 1 + 14
We consider the new divisor 46 and the new remainder 14,and apply the division lemma to get
46 = 14 x 3 + 4
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 978 and 346 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(46,14) = HCF(60,46) = HCF(286,60) = HCF(346,286) = HCF(978,346) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 2, we apply the division lemma to 32 and 2, to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 32 is 2
Notice that 2 = HCF(32,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 978, 346, 32?
Answer: HCF of 978, 346, 32 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 346, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 346, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.