Highest Common Factor of 978, 602 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 978, 602 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 602 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, 602 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, 602 is 2.
HCF(978, 602) = 2
HCF of 978, 602 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 602 is 2.
Highest Common Factor of 978,602 is 2
Step 1: Since 978 > 602, we apply the division lemma to 978 and 602, to get
978 = 602 x 1 + 376
Step 2: Since the reminder 602 ≠ 0, we apply division lemma to 376 and 602, to get
602 = 376 x 1 + 226
Step 3: We consider the new divisor 376 and the new remainder 226, and apply the division lemma to get
376 = 226 x 1 + 150
We consider the new divisor 226 and the new remainder 150,and apply the division lemma to get
226 = 150 x 1 + 76
We consider the new divisor 150 and the new remainder 76,and apply the division lemma to get
150 = 76 x 1 + 74
We consider the new divisor 76 and the new remainder 74,and apply the division lemma to get
76 = 74 x 1 + 2
We consider the new divisor 74 and the new remainder 2,and apply the division lemma to get
74 = 2 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 978 and 602 is 2
Notice that 2 = HCF(74,2) = HCF(76,74) = HCF(150,76) = HCF(226,150) = HCF(376,226) = HCF(602,376) = HCF(978,602) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 978, 602 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 978, 602?
Answer: HCF of 978, 602 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 602 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 602 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.