Highest Common Factor of 156, 420 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 156, 420 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 156, 420 is 12 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 156, 420 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 156, 420 is 12.
HCF(156, 420) = 12
HCF of 156, 420 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 156, 420 is 12.
Highest Common Factor of 156,420 is 12
Step 1: Since 420 > 156, we apply the division lemma to 420 and 156, to get
420 = 156 x 2 + 108
Step 2: Since the reminder 156 ≠ 0, we apply division lemma to 108 and 156, to get
156 = 108 x 1 + 48
Step 3: We consider the new divisor 108 and the new remainder 48, and apply the division lemma to get
108 = 48 x 2 + 12
We consider the new divisor 48 and the new remainder 12, and apply the division lemma to get
48 = 12 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 156 and 420 is 12
Notice that 12 = HCF(48,12) = HCF(108,48) = HCF(156,108) = HCF(420,156) .
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Frequently Asked Questions on HCF of 156, 420 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 156, 420?
Answer: HCF of 156, 420 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 156, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 156, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.