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 416, 464, 158 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 464, 158 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 416, 464, 158 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 416, 464, 158 is 2.
HCF(416, 464, 158) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 464, 158 is 2.
Step 1: Since 464 > 416, we apply the division lemma to 464 and 416, to get
464 = 416 x 1 + 48
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 48 and 416, to get
416 = 48 x 8 + 32
Step 3: We consider the new divisor 48 and the new remainder 32, and apply the division lemma to get
48 = 32 x 1 + 16
We consider the new divisor 32 and the new remainder 16, and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 416 and 464 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(416,48) = HCF(464,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 158 > 16, we apply the division lemma to 158 and 16, to get
158 = 16 x 9 + 14
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 14 and 16, to get
16 = 14 x 1 + 2
Step 3: We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 158 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(158,16) .
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 416, 464, 158?
Answer: HCF of 416, 464, 158 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 464, 158 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 464, 158 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.