Highest Common Factor of 164, 978, 753 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 164, 978, 753 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 164, 978, 753 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 164, 978, 753 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 164, 978, 753 is 1.
HCF(164, 978, 753) = 1
HCF of 164, 978, 753 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 164, 978, 753 is 1.
Highest Common Factor of 164,978,753 is 1
Step 1: Since 978 > 164, we apply the division lemma to 978 and 164, to get
978 = 164 x 5 + 158
Step 2: Since the reminder 164 ≠ 0, we apply division lemma to 158 and 164, to get
164 = 158 x 1 + 6
Step 3: We consider the new divisor 158 and the new remainder 6, and apply the division lemma to get
158 = 6 x 26 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 164 and 978 is 2
Notice that 2 = HCF(6,2) = HCF(158,6) = HCF(164,158) = HCF(978,164) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 753 > 2, we apply the division lemma to 753 and 2, to get
753 = 2 x 376 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 753 is 1
Notice that 1 = HCF(2,1) = HCF(753,2) .
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Frequently Asked Questions on HCF of 164, 978, 753 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 164, 978, 753?
Answer: HCF of 164, 978, 753 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 164, 978, 753 using Euclid's Algorithm?
Answer: For arbitrary numbers 164, 978, 753 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.