Highest Common Factor of 352, 480, 416 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 352, 480, 416 i.e. 32 the largest integer that leaves a remainder zero for all numbers.
HCF of 352, 480, 416 is 32 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 352, 480, 416 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 352, 480, 416 is 32.
HCF(352, 480, 416) = 32
HCF of 352, 480, 416 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 352, 480, 416 is 32.
Highest Common Factor of 352,480,416 is 32
Step 1: Since 480 > 352, we apply the division lemma to 480 and 352, to get
480 = 352 x 1 + 128
Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 128 and 352, to get
352 = 128 x 2 + 96
Step 3: We consider the new divisor 128 and the new remainder 96, and apply the division lemma to get
128 = 96 x 1 + 32
We consider the new divisor 96 and the new remainder 32, and apply the division lemma to get
96 = 32 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 352 and 480 is 32
Notice that 32 = HCF(96,32) = HCF(128,96) = HCF(352,128) = HCF(480,352) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 416 > 32, we apply the division lemma to 416 and 32, to get
416 = 32 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 32 and 416 is 32
Notice that 32 = HCF(416,32) .
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Frequently Asked Questions on HCF of 352, 480, 416 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 352, 480, 416?
Answer: HCF of 352, 480, 416 is 32 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 352, 480, 416 using Euclid's Algorithm?
Answer: For arbitrary numbers 352, 480, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.