Highest Common Factor of 916, 672, 749, 978 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 916, 672, 749, 978 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 916, 672, 749, 978 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 916, 672, 749, 978 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 916, 672, 749, 978 is 1.
HCF(916, 672, 749, 978) = 1
HCF of 916, 672, 749, 978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 916, 672, 749, 978 is 1.
Highest Common Factor of 916,672,749,978 is 1
Step 1: Since 916 > 672, we apply the division lemma to 916 and 672, to get
916 = 672 x 1 + 244
Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 244 and 672, to get
672 = 244 x 2 + 184
Step 3: We consider the new divisor 244 and the new remainder 184, and apply the division lemma to get
244 = 184 x 1 + 60
We consider the new divisor 184 and the new remainder 60,and apply the division lemma to get
184 = 60 x 3 + 4
We consider the new divisor 60 and the new remainder 4,and apply the division lemma to get
60 = 4 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 916 and 672 is 4
Notice that 4 = HCF(60,4) = HCF(184,60) = HCF(244,184) = HCF(672,244) = HCF(916,672) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 4, we apply the division lemma to 749 and 4, to get
749 = 4 x 187 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 749 is 1
Notice that 1 = HCF(4,1) = HCF(749,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 1, we apply the division lemma to 978 and 1, to get
978 = 1 x 978 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 978 is 1
Notice that 1 = HCF(978,1) .
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Frequently Asked Questions on HCF of 916, 672, 749, 978 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 916, 672, 749, 978?
Answer: HCF of 916, 672, 749, 978 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 916, 672, 749, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 916, 672, 749, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.