Highest Common Factor of 374, 978 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 374, 978 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 374, 978 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 374, 978 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 374, 978 is 2.
HCF(374, 978) = 2
HCF of 374, 978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 374, 978 is 2.
Highest Common Factor of 374,978 is 2
Step 1: Since 978 > 374, we apply the division lemma to 978 and 374, to get
978 = 374 x 2 + 230
Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 230 and 374, to get
374 = 230 x 1 + 144
Step 3: We consider the new divisor 230 and the new remainder 144, and apply the division lemma to get
230 = 144 x 1 + 86
We consider the new divisor 144 and the new remainder 86,and apply the division lemma to get
144 = 86 x 1 + 58
We consider the new divisor 86 and the new remainder 58,and apply the division lemma to get
86 = 58 x 1 + 28
We consider the new divisor 58 and the new remainder 28,and apply the division lemma to get
58 = 28 x 2 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 374 and 978 is 2
Notice that 2 = HCF(28,2) = HCF(58,28) = HCF(86,58) = HCF(144,86) = HCF(230,144) = HCF(374,230) = HCF(978,374) .
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Frequently Asked Questions on HCF of 374, 978 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 374, 978?
Answer: HCF of 374, 978 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 374, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 374, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.