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 742, 546, 118 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 546, 118 is 2 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 742, 546, 118 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 742, 546, 118 is 2.
HCF(742, 546, 118) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 742, 546, 118 is 2.
Step 1: Since 742 > 546, we apply the division lemma to 742 and 546, to get
742 = 546 x 1 + 196
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 196 and 546, to get
546 = 196 x 2 + 154
Step 3: We consider the new divisor 196 and the new remainder 154, and apply the division lemma to get
196 = 154 x 1 + 42
We consider the new divisor 154 and the new remainder 42,and apply the division lemma to get
154 = 42 x 3 + 28
We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get
42 = 28 x 1 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 742 and 546 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(154,42) = HCF(196,154) = HCF(546,196) = HCF(742,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 118 > 14, we apply the division lemma to 118 and 14, to get
118 = 14 x 8 + 6
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 6 and 14, to get
14 = 6 x 2 + 2
Step 3: 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 14 and 118 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(118,14) .
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 742, 546, 118?
Answer: HCF of 742, 546, 118 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 546, 118 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 546, 118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.