Highest Common Factor of 342, 135, 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 342, 135, 156 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 135, 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 342, 135, 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 342, 135, 156 is 3.
HCF(342, 135, 156) = 3
HCF of 342, 135, 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 342, 135, 156 is 3.
Highest Common Factor of 342,135,156 is 3
Step 1: Since 342 > 135, we apply the division lemma to 342 and 135, to get
342 = 135 x 2 + 72
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 72 and 135, to get
135 = 72 x 1 + 63
Step 3: We consider the new divisor 72 and the new remainder 63, and apply the division lemma to get
72 = 63 x 1 + 9
We consider the new divisor 63 and the new remainder 9, and apply the division lemma to get
63 = 9 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 342 and 135 is 9
Notice that 9 = HCF(63,9) = HCF(72,63) = HCF(135,72) = HCF(342,135) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 156 > 9, we apply the division lemma to 156 and 9, to get
156 = 9 x 17 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 156 is 3
Notice that 3 = HCF(9,3) = HCF(156,9) .
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Frequently Asked Questions on HCF of 342, 135, 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 342, 135, 156?
Answer: HCF of 342, 135, 156 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 135, 156 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 135, 156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.