Highest Common Factor of 411, 156 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 411, 156 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 411, 156 is 3 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 411, 156 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 411, 156 is 3.
HCF(411, 156) = 3
HCF of 411, 156 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 411, 156 is 3.
Highest Common Factor of 411,156 is 3
Step 1: Since 411 > 156, we apply the division lemma to 411 and 156, to get
411 = 156 x 2 + 99
Step 2: Since the reminder 156 ≠ 0, we apply division lemma to 99 and 156, to get
156 = 99 x 1 + 57
Step 3: We consider the new divisor 99 and the new remainder 57, and apply the division lemma to get
99 = 57 x 1 + 42
We consider the new divisor 57 and the new remainder 42,and apply the division lemma to get
57 = 42 x 1 + 15
We consider the new divisor 42 and the new remainder 15,and apply the division lemma to get
42 = 15 x 2 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 411 and 156 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(42,15) = HCF(57,42) = HCF(99,57) = HCF(156,99) = HCF(411,156) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 411, 156 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 411, 156?
Answer: HCF of 411, 156 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 411, 156 using Euclid's Algorithm?
Answer: For arbitrary numbers 411, 156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.