Highest Common Factor of 416, 975, 688 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 416, 975, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 975, 688 is 1 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, 975, 688 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, 975, 688 is 1.
HCF(416, 975, 688) = 1
HCF of 416, 975, 688 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 975, 688 is 1.
Highest Common Factor of 416,975,688 is 1
Step 1: Since 975 > 416, we apply the division lemma to 975 and 416, to get
975 = 416 x 2 + 143
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 143 and 416, to get
416 = 143 x 2 + 130
Step 3: We consider the new divisor 143 and the new remainder 130, and apply the division lemma to get
143 = 130 x 1 + 13
We consider the new divisor 130 and the new remainder 13, and apply the division lemma to get
130 = 13 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 416 and 975 is 13
Notice that 13 = HCF(130,13) = HCF(143,130) = HCF(416,143) = HCF(975,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 688 > 13, we apply the division lemma to 688 and 13, to get
688 = 13 x 52 + 12
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 12 and 13, to get
13 = 12 x 1 + 1
Step 3: We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 688 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(688,13) .
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Frequently Asked Questions on HCF of 416, 975, 688 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 416, 975, 688?
Answer: HCF of 416, 975, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 975, 688 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 975, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
