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 601, 978, 745 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 601, 978, 745 is 1 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 601, 978, 745 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 601, 978, 745 is 1.
HCF(601, 978, 745) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 601, 978, 745 is 1.
Step 1: Since 978 > 601, we apply the division lemma to 978 and 601, to get
978 = 601 x 1 + 377
Step 2: Since the reminder 601 ≠ 0, we apply division lemma to 377 and 601, to get
601 = 377 x 1 + 224
Step 3: We consider the new divisor 377 and the new remainder 224, and apply the division lemma to get
377 = 224 x 1 + 153
We consider the new divisor 224 and the new remainder 153,and apply the division lemma to get
224 = 153 x 1 + 71
We consider the new divisor 153 and the new remainder 71,and apply the division lemma to get
153 = 71 x 2 + 11
We consider the new divisor 71 and the new remainder 11,and apply the division lemma to get
71 = 11 x 6 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 601 and 978 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(71,11) = HCF(153,71) = HCF(224,153) = HCF(377,224) = HCF(601,377) = HCF(978,601) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 745 > 1, we apply the division lemma to 745 and 1, to get
745 = 1 x 745 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 745 is 1
Notice that 1 = HCF(745,1) .
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 601, 978, 745?
Answer: HCF of 601, 978, 745 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 601, 978, 745 using Euclid's Algorithm?
Answer: For arbitrary numbers 601, 978, 745 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.