Highest Common Factor of 1572, 2374 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 1572, 2374 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1572, 2374 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 1572, 2374 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 1572, 2374 is 2.
HCF(1572, 2374) = 2
HCF of 1572, 2374 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1572, 2374 is 2.
Highest Common Factor of 1572,2374 is 2
Step 1: Since 2374 > 1572, we apply the division lemma to 2374 and 1572, to get
2374 = 1572 x 1 + 802
Step 2: Since the reminder 1572 ≠ 0, we apply division lemma to 802 and 1572, to get
1572 = 802 x 1 + 770
Step 3: We consider the new divisor 802 and the new remainder 770, and apply the division lemma to get
802 = 770 x 1 + 32
We consider the new divisor 770 and the new remainder 32,and apply the division lemma to get
770 = 32 x 24 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1572 and 2374 is 2
Notice that 2 = HCF(32,2) = HCF(770,32) = HCF(802,770) = HCF(1572,802) = HCF(2374,1572) .
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Frequently Asked Questions on HCF of 1572, 2374 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 1572, 2374?
Answer: HCF of 1572, 2374 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1572, 2374 using Euclid's Algorithm?
Answer: For arbitrary numbers 1572, 2374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.