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, 456, 141 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 164, 456, 141 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, 456, 141 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, 456, 141 is 1.
HCF(164, 456, 141) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 164, 456, 141 is 1.
Step 1: Since 456 > 164, we apply the division lemma to 456 and 164, to get
456 = 164 x 2 + 128
Step 2: Since the reminder 164 ≠ 0, we apply division lemma to 128 and 164, to get
164 = 128 x 1 + 36
Step 3: We consider the new divisor 128 and the new remainder 36, and apply the division lemma to get
128 = 36 x 3 + 20
We consider the new divisor 36 and the new remainder 20,and apply the division lemma to get
36 = 20 x 1 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 164 and 456 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(128,36) = HCF(164,128) = HCF(456,164) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 141 > 4, we apply the division lemma to 141 and 4, to get
141 = 4 x 35 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 141 is 1
Notice that 1 = HCF(4,1) = HCF(141,4) .
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 164, 456, 141?
Answer: HCF of 164, 456, 141 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 164, 456, 141 using Euclid's Algorithm?
Answer: For arbitrary numbers 164, 456, 141 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.